How many zeroes does a linear equation have ?? -Maths 9th

How many zeroes does a linear equation have ?? -Maths 9th
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Answer :

A linear equation in one variable is having only 1 zero or one solution. But a linear Equation with 2 or more variables is having infinitely many solutions .. because there are infinite rational numbers.
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One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Description : One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Last Answer : (b) Let p (x) = 2x2 + 7x-4 = 2x2 + 8x-x-4 [by splitting middle term] = 2x(x+ 4)-1(x+ 4) = (2x-1)(x+ 4) For zeroes of p(x), put p(x) = 0 ⇒ (2x -1) (x + 4) = 0 ⇒ 2x-1 = 0 and x+4 = 0 ⇒ x = 1/2 and x = -4 Hence, one of the zeroes of the polynomial p(x) is 1/2.

Find the zeroes of the polynomial in each of the following, -Maths 9th

Description : Find the zeroes of the polynomial in each of the following, -Maths 9th

Last Answer : (i) Given, polynomial is p(x) = x- 4 For zero of polynomial, put p(x) = x-4 = 0 ⇒ x= 4 Hence, zero of polynomial is 4. (ii) Given, polynomial is g(x) = 3-6x For zero of polynomial, put g(x) ... polynomial h(y) = 2 y For zero of polynomial, put h(y) = 0 2y= 0 Hence, the zero of polynomial is 0,

Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Description : Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Last Answer : Given, polynomial is p(x) = (x – 2)2 – (x+ 2)2 For zeroes of polynomial, put p(x) = 0 (x – 2)2 – (x+ 2)2 = 0 (x-2 + x+2)(x-2-x-2) = 0 [using identity, a2-b2 =(a-b)(a + b)] ⇒ (2x)(-4) = 0

One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Description : One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Last Answer : (b) Let p (x) = 2x2 + 7x-4 = 2x2 + 8x-x-4 [by splitting middle term] = 2x(x+ 4)-1(x+ 4) = (2x-1)(x+ 4) For zeroes of p(x), put p(x) = 0 ⇒ (2x -1) (x + 4) = 0 ⇒ 2x-1 = 0 and x+4 = 0 ⇒ x = 1/2 and x = -4 Hence, one of the zeroes of the polynomial p(x) is 1/2.

Find the zeroes of the polynomial in each of the following, -Maths 9th

Description : Find the zeroes of the polynomial in each of the following, -Maths 9th

Last Answer : (i) Given, polynomial is p(x) = x- 4 For zero of polynomial, put p(x) = x-4 = 0 ⇒ x= 4 Hence, zero of polynomial is 4. (ii) Given, polynomial is g(x) = 3-6x For zero of polynomial, put g(x) ... polynomial h(y) = 2 y For zero of polynomial, put h(y) = 0 2y= 0 Hence, the zero of polynomial is 0,

Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Description : Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Last Answer : Given, polynomial is p(x) = (x – 2)2 – (x+ 2)2 For zeroes of polynomial, put p(x) = 0 (x – 2)2 – (x+ 2)2 = 0 (x-2 + x+2)(x-2-x-2) = 0 [using identity, a2-b2 =(a-b)(a + b)] ⇒ (2x)(-4) = 0

If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Description : If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Last Answer : p(x) = (k2 – 14) x2 – 2x – 12 Here a = k2 – 14, b = -2, c = -12 Sum of the zeroes, (α + β) = 1 …[Given] ⇒ − = 1 ⇒ −(−2)2−14 = 1 ⇒ k2 – 14 = 2 ⇒ k2 = 16 ⇒ k = ±4

If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k. -Maths 9th

Description : If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k. -Maths 9th

Last Answer : Here a = 3, b = -k, c = 6 Sum of the zeroes, (α + β) = − = 3 …..(given) ⇒ −(−)3 = 3 ⇒ k = 9

What is the general form of linear equation in two variables ? -Maths 9th

Description : What is the general form of linear equation in two variables ? -Maths 9th

Last Answer : The general form of linear equation in two variables can be written as: ax+by+c=0

The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th

Description : The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th

Last Answer : Given, point (2,3) lies on the line. So, the point (2, 3) is the solution of 3x - (a -1) y = 2a - 1 On putting x = 2 and y = 3 in given solution. ∴ 3 2 - (a-1) 3 = 2a - 1 ⇒ 6 - 3a + 3 = 2a - 1 ⇒ - 3a ... 2 2) 3 = 3b ⇒ 10 - 9 = 3b ⇒ 1 = 3b ⇒ 1 / 3 = b Hence, the value of b is 1 / 3.

The linear equation 2x – 5y = 7 has -Maths 9th

Description : The linear equation 2x – 5y = 7 has -Maths 9th

Last Answer : (c) In the given equation 2x – 5y = 7, for every value of x, we get a corresponding value of y and vice-versa. Therefore, the linear equation has infinitely many solutions.

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Description : If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Last Answer : (a) Since, (2, 0) is a solution of the given linear equation 2x + 3y = k, then put x =2 and y= 0 in the equation. ⇒ 2 (2) + 3 (0) = k ⇒ k = 4 Hence, the value of k is 4.

Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form -Maths 9th

Description : Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form -Maths 9th

Last Answer : (a) The given linear equation is 2x + 0y + 9 = 0 ⇒ 2x + 9 = 0 ⇒ 2x = -9 ⇒ x= - 9/2 and y can be any real number. Hence, (-9/2 , m) is the required form of solution of the given linear equation.

The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point. -Maths 9th

Last Answer : (d) Since, the graph of linear equation 2x + 3y = 6 cuts the Y-axis. So, we put x = 0 in the given equation 2x+ 3y = 6, we get 2 x 0+ 3y = 6 ⇒ 3y = 6 y = 2. Hence, at the point (0, 2), the given linear equation cuts the Y-axis.

x = 5 and y = 2 is a solution of the linear equation. -Maths 9th

Description : x = 5 and y = 2 is a solution of the linear equation. -Maths 9th

Last Answer : (c) (a) Take x + 2y, on putting x=5 and y = 2, we get 5 + 2(2) = 5+ 4 = 9≠7. So, (5, 2) is not a solution of x + 2y = 7 (b) Take 5x + 2y, on putting x = 5 and y = 2, we get 5x 5 + 2 x2 =25+ 4 = ... on putting x = 5 and y = 2, we get 5 5 + 2=25 + 2 =27 ≠7 So, (5, 2) is not a solution of 5x + y = 7.

If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th

Description : If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th

Last Answer : (b) Let us consider a linear equation ax + by + c = 0 (i) Since, (-2,2), (0, 0) and (2, -2) are the solutions of linear equation therefore it satisfies the Eq. (i), we get At point(-2,2), -2a + 2b + c ... b(x + y)= 0 ⇒ x + y = 0, b ≠ 0 Hence, x + y= 0 is the required form of the linear equation.

The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Last Answer : (c) Since, the graph of linear equation 2x + 3y = 6 meets the X-axis. So, we put y = 0 in 2x + 3y = 6 ⇒ 2x + 3(0) = 6 = 2x + 0 = 6 ⇒ x = 6/2 ⇒ x = 3 Hence, the coordinate on X-axis is (3, 0).

The graph of the linear equation y = x passes through the point. -Maths 9th

Description : The graph of the linear equation y = x passes through the point. -Maths 9th

Last Answer : (c) The linear equation y = x has same value of x and y-coordinates are same. Therefore, the point (1,1) must lie on the line y = x.

If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation. -Maths 9th

Description : If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation. -Maths 9th

Last Answer : (b) By property, if we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation remains the same i.e., the solution of the linear equation is remains unchanged.

Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units. -Maths 9th

Description : Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units. -Maths 9th

Last Answer : As per question, the sum of the coordinates is 10 units. Let x and y be two coordinates, then we get x + y = 10. For x = 5, y = 5, therefore, (5, 5) lies on the graph of x + y = 10. For x = ... and (3, 7) on the graph paper and joining them by a line, we get graph of the linear equation x + y = 10.

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. -Maths 9th

Description : Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. -Maths 9th

Last Answer : Let the abscissa of the point be x, According to the question, Ordinate (y) = 3 x Abscissa ⇒ y=3x When x = 1, then y = 3 x 1 = 3 and when x = 2, then y = 3 x 2 = 6. Here, ... the line AB. Hence, y = 3x is the required equation such that each point on its graph has an ordinate 3 times its abscissa.

Find the solution of the linear equation x+2y = 8 which represents a point on -Maths 9th

Description : Find the solution of the linear equation x+2y = 8 which represents a point on -Maths 9th

Last Answer : We have, x + 2y = 8 ,..(i) (i) When the point is on the X-axis, then put y = 0 in Eq. (i), we get x+2 (0)=8 ⇒ x = 8 Hence, the required point is (8, 0). (ii) When the point is on the Y-axis, then put x = 0 in Eq. (i), we get 0 + 2y = 8 ⇒ y = 8/2 = 4 Hence, the required point is (0, 4).

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Last Answer : The given linear equation is 2x + cy= 8. …(i) Now, by condition, x and y-coordinate of given linear equation are same, i.e., x = y. Put y = x in Eq. (i), we get

Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is value of y when x = 5 ? -Maths 9th

Description : Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is value of y when x = 5 ? -Maths 9th

Last Answer : Linear equation

The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th

Description : The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th

Last Answer : Given, point (2,3) lies on the line. So, the point (2, 3) is the solution of 3x - (a -1) y = 2a - 1 On putting x = 2 and y = 3 in given solution. ∴ 3 2 - (a-1) 3 = 2a - 1 ⇒ 6 - 3a + 3 = 2a - 1 ⇒ - 3a ... 2 2) 3 = 3b ⇒ 10 - 9 = 3b ⇒ 1 = 3b ⇒ 1 / 3 = b Hence, the value of b is 1 / 3.

The linear equation 2x – 5y = 7 has -Maths 9th

Description : The linear equation 2x – 5y = 7 has -Maths 9th

Last Answer : (c) In the given equation 2x – 5y = 7, for every value of x, we get a corresponding value of y and vice-versa. Therefore, the linear equation has infinitely many solutions.

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Description : If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Last Answer : (a) Since, (2, 0) is a solution of the given linear equation 2x + 3y = k, then put x =2 and y= 0 in the equation. ⇒ 2 (2) + 3 (0) = k ⇒ k = 4 Hence, the value of k is 4.

Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form -Maths 9th

Description : Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form -Maths 9th

Last Answer : (a) The given linear equation is 2x + 0y + 9 = 0 ⇒ 2x + 9 = 0 ⇒ 2x = -9 ⇒ x= - 9/2 and y can be any real number. Hence, (-9/2 , m) is the required form of solution of the given linear equation.

The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point. -Maths 9th

Last Answer : (d) Since, the graph of linear equation 2x + 3y = 6 cuts the Y-axis. So, we put x = 0 in the given equation 2x+ 3y = 6, we get 2 x 0+ 3y = 6 ⇒ 3y = 6 y = 2. Hence, at the point (0, 2), the given linear equation cuts the Y-axis.

x = 5 and y = 2 is a solution of the linear equation. -Maths 9th

Description : x = 5 and y = 2 is a solution of the linear equation. -Maths 9th

Last Answer : (c) (a) Take x + 2y, on putting x=5 and y = 2, we get 5 + 2(2) = 5+ 4 = 9≠7. So, (5, 2) is not a solution of x + 2y = 7 (b) Take 5x + 2y, on putting x = 5 and y = 2, we get 5x 5 + 2 x2 =25+ 4 = ... on putting x = 5 and y = 2, we get 5 5 + 2=25 + 2 =27 ≠7 So, (5, 2) is not a solution of 5x + y = 7.

If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th

Description : If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th

Last Answer : (b) Let us consider a linear equation ax + by + c = 0 (i) Since, (-2,2), (0, 0) and (2, -2) are the solutions of linear equation therefore it satisfies the Eq. (i), we get At point(-2,2), -2a + 2b + c ... b(x + y)= 0 ⇒ x + y = 0, b ≠ 0 Hence, x + y= 0 is the required form of the linear equation.

The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Last Answer : (c) Since, the graph of linear equation 2x + 3y = 6 meets the X-axis. So, we put y = 0 in 2x + 3y = 6 ⇒ 2x + 3(0) = 6 = 2x + 0 = 6 ⇒ x = 6/2 ⇒ x = 3 Hence, the coordinate on X-axis is (3, 0).

The graph of the linear equation y = x passes through the point. -Maths 9th

Description : The graph of the linear equation y = x passes through the point. -Maths 9th

Last Answer : (c) The linear equation y = x has same value of x and y-coordinates are same. Therefore, the point (1,1) must lie on the line y = x.

If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation. -Maths 9th

Description : If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation. -Maths 9th

Last Answer : (b) By property, if we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation remains the same i.e., the solution of the linear equation is remains unchanged.

Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units. -Maths 9th

Description : Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units. -Maths 9th

Last Answer : As per question, the sum of the coordinates is 10 units. Let x and y be two coordinates, then we get x + y = 10. For x = 5, y = 5, therefore, (5, 5) lies on the graph of x + y = 10. For x = ... and (3, 7) on the graph paper and joining them by a line, we get graph of the linear equation x + y = 10.

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. -Maths 9th

Description : Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. -Maths 9th

Last Answer : Let the abscissa of the point be x, According to the question, Ordinate (y) = 3 x Abscissa ⇒ y=3x When x = 1, then y = 3 x 1 = 3 and when x = 2, then y = 3 x 2 = 6. Here, ... the line AB. Hence, y = 3x is the required equation such that each point on its graph has an ordinate 3 times its abscissa.

Find the solution of the linear equation x+2y = 8 which represents a point on -Maths 9th

Description : Find the solution of the linear equation x+2y = 8 which represents a point on -Maths 9th

Last Answer : We have, x + 2y = 8 ,..(i) (i) When the point is on the X-axis, then put y = 0 in Eq. (i), we get x+2 (0)=8 ⇒ x = 8 Hence, the required point is (8, 0). (ii) When the point is on the Y-axis, then put x = 0 in Eq. (i), we get 0 + 2y = 8 ⇒ y = 8/2 = 4 Hence, the required point is (0, 4).

For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th

Last Answer : The given linear equation is 2x + cy= 8. …(i) Now, by condition, x and y-coordinate of given linear equation are same, i.e., x = y. Put y = x in Eq. (i), we get

Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is value of y when x = 5 ? -Maths 9th

Description : Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is value of y when x = 5 ? -Maths 9th

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Description : Write a solution of the linear equation 5x + 0y +8 = 0 in two variables. -Maths 9th

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Is ax + by + c = 0, where a, b and c are real numbers, a linear equation in two variables? Give reason. -Maths 9th

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Express the given statement in the form of a linear equation in two variables. The sum of the ordinate and abscissa of a point is 6. -Maths 9th

Description : Express the given statement in the form of a linear equation in two variables. The sum of the ordinate and abscissa of a point is 6. -Maths 9th

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Express the given equation as linear equation in two variables in standard form: 3y = 2x. -Maths 9th

Description : Express the given equation as linear equation in two variables in standard form: 3y = 2x. -Maths 9th

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In some countries temperature is measured in Fahrenheit, whereas in countries like India it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: F = 9/5 C+ 32. If the temperature is 30°C, then what is the temperature in Fahrenheit? -Maths 9th

Description : In some countries temperature is measured in Fahrenheit, whereas in countries like India it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: F = 9/5 C+ 32. If the temperature is 30°C, then what is the temperature in Fahrenheit? -Maths 9th

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Arvind and Vinod have some erasers. Arvind said to Vinod, if you will give me 10 erasers, I will have twice the erasers left with you. Represent this situation as a linear equation in two variables. -Maths 9th

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Write any two solutions of the linear equation 3x + 2y =9. -Maths 9th

Description : Write any two solutions of the linear equation 3x + 2y =9. -Maths 9th

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Determine the point on the graph of the linear equation x + y = 6, whose ordinate is 2 times its abscissa. -Maths 9th

Description : Determine the point on the graph of the linear equation x + y = 6, whose ordinate is 2 times its abscissa. -Maths 9th

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For what value of c, the linear equation 2x + cy = 8 has equal values of x and y as its solution? -Maths 9th

Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y as its solution? -Maths 9th

Last Answer : Solution :-

Force applied on a body of mass 5 kg is directly proportional to the acceleration produced in the body. Represent this solution as a linear equation in two variables. -Maths 9th

Description : Force applied on a body of mass 5 kg is directly proportional to the acceleration produced in the body. Represent this solution as a linear equation in two variables. -Maths 9th

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If the length of a rectangle is decreased by 3 units and breadth increased by 4 unit, then the area will increase by 9 sq. units. Represent this situation as a linear equation in two variables. -Maths 9th

Description : If the length of a rectangle is decreased by 3 units and breadth increased by 4 unit, then the area will increase by 9 sq. units. Represent this situation as a linear equation in two variables. -Maths 9th

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