If – x^2 + 3x + 4 > 0, then which of the following is correct? -Maths 9th

If – x^2 + 3x + 4 > 0, then which of the following is correct? -Maths 9th
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If x is real and x^2 + 3x + 2 > 0, x^2 – 3x – 4 < 0, then which of the following is correct? -Maths 9th

Description : If x is real and x^2 + 3x + 2 > 0, x^2 – 3x – 4 < 0, then which of the following is correct? -Maths 9th

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If x+1 is a factor of the polynomial 3x(square) - kx,then find the value of k. -Maths 9th

Description : If x+1 is a factor of the polynomial 3x(square) - kx,then find the value of k. -Maths 9th

Last Answer : Solution :-

If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

Description : If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

Last Answer : -2/5 is value of a

If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

Description : If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

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If 5^(3x^2 log10 2) = 2^((x+1/2)log10 25), then the value of x is: -Maths 9th

Description : If 5^(3x^2 log10 2) = 2^((x+1/2)log10 25), then the value of x is: -Maths 9th

Last Answer : (d) \(-rac{1}{3}\)\(5^{{3x^2}log_{10}2}\) = 2\(\big(x+rac{1}{2}\big)\)log10 25⇒ \(5^{{3x^2}log_{10}2}\) = 2\(\big(rac{2x+1}{2}\big)\) x log10 5 = 2(2x+1)log10 5⇒ \(5^{{3x^2}log_{10}2}\) = 2(2x+1)log2 5. ... aloga x = x]⇒ 3x2 = 2x + 1 ⇒ 3x2 - 2x - 1 = 0 ⇒ (x - 1) (3x + 1) = 0⇒ x = 1, \(-rac{1}{3}\)

If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Description : If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Last Answer : Given that the following polynomials leave the same remainder when divided by (x - 4) : We are to find the value of a. Remainder theorem: When (x - b) divides a polynomial p(x), then the remainder is p(b). So, from (i) and (ii), we get Thus, the required value of a is 1.

If cosec |=3x and cot |=3/x. then find the value of (x2-1/x2) -Maths 9th

Description : If cosec |=3x and cot |=3/x. then find the value of (x2-1/x2) -Maths 9th

Last Answer : cosecβ = = 3X and cotβ = 3/X , to find value ( X2 - 1/X2 ) . we know , cosec2β = cot2β +1 putting value , (3X )2 = ( 3/X )2 +1 , OR 9X2 = 9 /X2 + 1 , OR 9X2 – 9/X2 = 1, OR 9( X2 - 1/X2 ) = 1, SO (X2 – 1/X2 ) = 1/9

Draw a graph of the equation x + Y = 5 & 3x - 2y =0 on the same graph paper. Find the coordinates of the point whose two lines intersect. -Maths 9th

Description : Draw a graph of the equation x + Y = 5 & 3x - 2y =0 on the same graph paper. Find the coordinates of the point whose two lines intersect. -Maths 9th

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Draw a graph of the equation x+ y=5 & 3x -2y=0 in the same graph paper find the coordinates of the point whose two two lines intersect. -Maths 9th

Description : Draw a graph of the equation x+ y=5 & 3x -2y=0 in the same graph paper find the coordinates of the point whose two two lines intersect. -Maths 9th

Last Answer : From x + y = 5, If x = 0 0 + y = 5 y = 5 Therefore (0,5) If x = 1 1 + y = 5 y =5 - 1 y = 4 Therefore (1,4) Draw a graph for this And From 3x - 2y = 0 If x = 0 3 (0) - 2y = 0 0 - ... 2y = 0 -2y = -6 y = -6/-2 y = 3 Therefore (2,3) Draw a graph for these points And the point of intersection is (2,3)

Find the range of values of x which satisfy x^2 + 6x – 27 > 0, –x^2 + 3x + 4 > 0 simultaneously. -Maths 9th

Description : Find the range of values of x which satisfy x^2 + 6x – 27 > 0, –x^2 + 3x + 4 > 0 simultaneously. -Maths 9th

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Which of the following values of x do not satisfy the inequality x^2 – 3x + 2 > 0 at all. -Maths 9th

Description : Which of the following values of x do not satisfy the inequality x^2 – 3x + 2 > 0 at all. -Maths 9th

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The set of values of x for which the inequalities x^2 – 3x – 10 < 0, 10x – x^2 – 16 > 0 hold simultaneously is -Maths 9th

Description : The set of values of x for which the inequalities x^2 – 3x – 10 < 0, 10x – x^2 – 16 > 0 hold simultaneously is -Maths 9th

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The equation whose roots are the negatives of the roots of the equation x^7 + 3x^5 + x^3 – x^2 + 7x + 2 = 0 is : -Maths 9th

Description : The equation whose roots are the negatives of the roots of the equation x^7 + 3x^5 + x^3 – x^2 + 7x + 2 = 0 is : -Maths 9th

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The equation whose roots are twice the roots of the equation x^2 – 3x + 3 = 0 is -Maths 9th

Description : The equation whose roots are twice the roots of the equation x^2 – 3x + 3 = 0 is -Maths 9th

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What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th

Description : What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th

Last Answer : (c) (8, 6)Let AB be the given line 4x + 3y = 25 Let O′(a, b) be the image of O in the given line AB. Let O O′ cut AB in point P. Also OP ⊥ AB and P is the mid-point of OO′. ∴ Co-ordinates of P are \(\bigg( ... 4 imes6}{3}\) = 8∴ The image of the point O(0, 0) in the line 4x + 3y - 25 = 0 is (8, 6).

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 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.

p(x)=x3+3x2+3x+1, g(x) = x+2 -Maths 9th

Description : p(x)=x3+3x2+3x+1, g(x) = x+2 -Maths 9th

Last Answer : p(x) = x3+3x2+3x+1, g(x) = x+2 g(x) = 0 ⇒ x+2 = 0 ⇒ x = −2 ∴ Zero of g(x) is -2. Now, p(−2) = (−2)3+3(−2)2+3(−2)+1 = −8+12−6+1 = −1 ≠ 0 ∴By factor theorem, g(x) is not a factor of p(x

Without actual division, prove that 2x4 – 5x3 + 2x2 – x+ 2 is divisible by x2-3x+2. -Maths 9th

Description : Without actual division, prove that 2x4 – 5x3 + 2x2 – x+ 2 is divisible by x2-3x+2. -Maths 9th

Last Answer : Let p(x) = 2x4 - 5x3 + 2x2 - x+ 2 firstly, factorise x2-3x+2. Now, x2-3x+2 = x2-2x-x+2 [by splitting middle term] = x(x-2)-1 (x-2)= (x-1)(x-2) Hence, 0 of x2-3x+2 are land 2. We have to prove that, 2x4 ... )2 - 2 + 2 = 2x16-5x8+2x4+ 0 = 32 - 40 + 8 = 40 - 40 =0 Hence, p(x) is divisible by x2-3x+2.

Without actual division, prove that 2x4 – 5x3 + 2x2 – x+ 2 is divisible by x2-3x+2. -Maths 9th

Description : Without actual division, prove that 2x4 – 5x3 + 2x2 – x+ 2 is divisible by x2-3x+2. -Maths 9th

Last Answer : Let p(x) = 2x4 - 5x3 + 2x2 - x+ 2 firstly, factorise x2-3x+2. Now, x2-3x+2 = x2-2x-x+2 [by splitting middle term] = x(x-2)-1 (x-2)= (x-1)(x-2) Hence, 0 of x2-3x+2 are land 2. We have to prove that, 2x4 ... )2 - 2 + 2 = 2x16-5x8+2x4+ 0 = 32 - 40 + 8 = 40 - 40 =0 Hence, p(x) is divisible by x2-3x+2.

What must be substract from x(to the power 4) + 3x(cube) + 4x(square) - 3x - 6 to get 3x(cube) + 4x(square) - x + 3? -Maths 9th

Description : What must be substract from x(to the power 4) + 3x(cube) + 4x(square) - 3x - 6 to get 3x(cube) + 4x(square) - x + 3? -Maths 9th

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What must be added to 2x(square) - 5x + 6 to get x(cube) - 3x(square) + 3x - 5? -Maths 9th

Description : What must be added to 2x(square) - 5x + 6 to get x(cube) - 3x(square) + 3x - 5? -Maths 9th

Last Answer : Solution :-

Find the remainder when f(x)=9x(cube) -x 3x(square) + 14x - 3 is divided by g(x)=(3x-1). -Maths 9th

Description : Find the remainder when f(x)=9x(cube) -x 3x(square) + 14x - 3 is divided by g(x)=(3x-1). -Maths 9th

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Find the coordinate where the linear equation 3x -4y = 11 meets at x-axis. -Maths 9th

Description : Find the coordinate where the linear equation 3x -4y = 11 meets at x-axis. -Maths 9th

Last Answer : hope it helps

Draw the graph of the linear equation 3x + 4y = 6. At what points, does the graph cut the x-axis and the y-axis? -Maths 9th

Description : Draw the graph of the linear equation 3x + 4y = 6. At what points, does the graph cut the x-axis and the y-axis? -Maths 9th

Last Answer : hope it helps

Solve for x: Sol. 3x/7 + 2/7 + 4(x + 1)/5 = 2/3(2x + 1) -Maths 9th

Description : Solve for x: Sol. 3x/7 + 2/7 + 4(x + 1)/5 = 2/3(2x + 1) -Maths 9th

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Two opposite angles of a ||gm are (60–x) degree and (3x –4) degree. Find the measure of each angles of the IIgm. -Maths 9th

Description : Two opposite angles of a ||gm are (60–x) degree and (3x –4) degree. Find the measure of each angles of the IIgm. -Maths 9th

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Draw the graph of the following equations (1) Y =3x+2 (b) Y=x -Maths 9th

Description : Draw the graph of the following equations (1) Y =3x+2 (b) Y=x -Maths 9th

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Find the value of the polynomial p(x) = x^3-3x^2-2x+6 at x = underroot 2 -Maths 9th

Description : Find the value of the polynomial p(x) = x^3-3x^2-2x+6 at x = underroot 2 -Maths 9th

Last Answer : In this chapter, we shall proceed with recalling some of the constructions already learnt in the earlier classes and deal with some more. Here in this section, we will construct some of these ... be done? 2. Always explain the construction. Write the sequence of steps that are actually taken.

Divide 3x^3 – 2x^2 – 19x + 22 by (x – 2) -Maths 9th

Description : Divide 3x^3 – 2x^2 – 19x + 22 by (x – 2) -Maths 9th

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For what value of m will the expression 3x^3 + mx^2 + 4x – 4m be divisible by x + 2 ? -Maths 9th

Description : For what value of m will the expression 3x^3 + mx^2 + 4x – 4m be divisible by x + 2 ? -Maths 9th

Last Answer : f(x) = 3x3 + mx2 + 4x – 4m f(x) is divisible by (x + 2) if f(–2) = 0 Now f(–2) = 3(–2)3 + m(–2)2 + 4(–2) – 4m = – 24 + 4m – ... ; 4m = – 32 ≠ 0 ∴ No such value of m exists for which (x + 2) is a factor of the given expression

Without actual division show that 2x^4 – 6x^3 + 3x^2 + 3x – 2 is exactly divisible by x^2 – 3x + 2 -Maths 9th

Description : Without actual division show that 2x^4 – 6x^3 + 3x^2 + 3x – 2 is exactly divisible by x^2 – 3x + 2 -Maths 9th

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Without actual division, show that (x – 1)^2n – x^2n + 2x – 1 is divisible by 2x^3 – 3x^2 + x. -Maths 9th

Description : Without actual division, show that (x – 1)^2n – x^2n + 2x – 1 is divisible by 2x^3 – 3x^2 + x. -Maths 9th

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For what value of k, will the expression (3x^3 – kx^2 + 4x + 16) be divisible by (x – k/2) ? -Maths 9th

Description : For what value of k, will the expression (3x^3 – kx^2 + 4x + 16) be divisible by (x – k/2) ? -Maths 9th

Last Answer : Given f(x) = 3x³ - kx² + 4x + 16. Since (x - k/2) is a factor of polynomial. This means x = k/2 is the zero of the given polynomial. ⇒ f(k/2) = 3(k/2)³ - k(k/2)² + 4(k/2) + 16 ⇒ 0 ... - 4k + 32) + 4(k² - 4k + 32) ⇒ 0 = (k + 4)(k² - 4k + 32) ⇒ k = -4.

If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Description : If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Last Answer : Given ax^3 + 4x^2 + 3x - 4 and x^3 - 4x + a leave the same remainder when divided by x - 3. Let p(x) = ax^3 + 4x^2 + 3x - 4 and g(x) = x^3 - 4x + a By remainder theorem, if f(x) is divided by (x − a) then ... 4 27a+41 g(3)=27-4(3)+a 15+a f(3)=G(3) 27a+41=15+a 26a=15-41 a=15-41/26 a=-26/26 a=-1

f(x) = x^4 – 2x^3 + 3x^2 – ax + b is a polynomial such that when it is divided by (x – 1) and (x + 1), the remainders are respectively 5 and 19. -Maths 9th

Description : f(x) = x^4 – 2x^3 + 3x^2 – ax + b is a polynomial such that when it is divided by (x – 1) and (x + 1), the remainders are respectively 5 and 19. -Maths 9th

Last Answer : answer:

What is (x^2-3x+2)/(x^2-5x +6)÷(x^2-5x+4)/(x^2-7x+12) equal to? -Maths 9th

Description : What is (x^2-3x+2)/(x^2-5x +6)÷(x^2-5x+4)/(x^2-7x+12) equal to? -Maths 9th

Last Answer : answer:

Find the equation of the straight line passing through the point (4, 5) and perpendicular to 3x – 2y + 5 = 0. -Maths 9th

Description : Find the equation of the straight line passing through the point (4, 5) and perpendicular to 3x – 2y + 5 = 0. -Maths 9th

Last Answer : There are two ways to prove it. 1st way: Area of triangle formed by the given points = 0 if they are collinear.∴ \(rac{1}{2}\) [\(x\)(2 - (y + 1) ) + 1((y + 1) - 1) + 0(1 - 2)] = 0⇒ \(rac{1}{2}\) [2\(x\) - \(x\)y - \( ... y - \(x\)y - 1 + \(x\) ⇒ x + y = \(x\)y ⇒ \(rac{1}{x}\) + \(rac{1}{y}\) = 1.

A straight line is parallel to the lines 3x – y – 3 = 0 and 3x – y + 5 = 0 and lies between them. -Maths 9th

Description : A straight line is parallel to the lines 3x – y – 3 = 0 and 3x – y + 5 = 0 and lies between them. -Maths 9th

Last Answer : (c) 3x - 4y + 15 = 0 Let (m > 0) be the gradient (slope) of the required line. Then, Equation of any line through (-5, 0) having slope = m is y - 0 = m(x - (-5)) or mx - y + 5m = 0 ...(i) Its ... (rac{3}{4}\) (∵ m is +ve)∴ Required equation: y = \(rac{3}{4}\) (x + 5)⇒ 3x - 4y + 15 = 0.

3. Check whether 7+3x is a factor of 3x3+7x. -Maths 9th

Description : 3. Check whether 7+3x is a factor of 3x3+7x. -Maths 9th

Last Answer : Solution: 7+3x = 0 ⇒ 3x = −7 ⇒ x = -7/3 ∴Remainder: 3(-7/3)3+7(-7/3) = -(343/9)+(-49/3) = (-343-(49)3)/9 = (-343-147)/9 = -490/9 ≠ 0 ∴7+3x is not a factor of 3x3+7x

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) 4x2–3x+7 -Maths 9th

Description : Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) 4x2–3x+7 -Maths 9th

Last Answer : Solution: The equation 4x2–3x+7 can be written as 4x2–3x1+7x0 Since x is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers, we can say that the expression 4x2–3x+7 is a polynomial in one variable

find 2 different solutions for 3x-8y=27 -Maths 9th

Description : find 2 different solutions for 3x-8y=27 -Maths 9th

Last Answer : Solving for first solution: 3x-8y=27 put the value of y=0 3x-8(0)=27 3x=27 x=27/3 therefore,x=9 so, first solution=(9,0). Solving for second solution: 3x-8y=27 put the value of x=1 3(1)-8y=27 3-8y=27 -8y=27-3 -8y=24 y= -24/8 y= -3 therefore, second solution=(1,-3). [answer].

In the given figure , two opposite angles of a parallelograms PQRS are (3x - 4)° and (56 - 3x)° . Find all the angles of given parallelogram . -Maths 9th

Description : In the given figure , two opposite angles of a parallelograms PQRS are (3x - 4)° and (56 - 3x)° . Find all the angles of given parallelogram . -Maths 9th

Last Answer : We know that opposite angles of a paralleloram are equal . ∴ ∠P = ∠R ⇒ 3x - 4 = 56 - 3x ⇒ 6x = 60 ⇒ x = 10 Thus, ∠P = ∠R = 3 10 - 4 = 26° Also, ∠P + ∠Q = 180° [ ... Hence, the four angles of the parallelogram PQRS are 26°, 154°,26° and 154°. We should care our earth to have good eco balance.

find 2 different solutions for 3x-8y=27 -Maths 9th

Description : find 2 different solutions for 3x-8y=27 -Maths 9th

Last Answer : Solving for first solution: 3x-8y=27 put the value of y=0 3x-8(0)=27 3x=27 x=27/3 therefore,x=9 so, first solution=(9,0). Solving for second solution: 3x-8y=27 put the value of x=1 3(1)-8y=27 3-8y=27 -8y=27-3 -8y=24 y= -24/8 y= -3 therefore, second solution=(1,-3). [answer].

In the given figure , two opposite angles of a parallelograms PQRS are (3x - 4)° and (56 - 3x)° . Find all the angles of given parallelogram . -Maths 9th

Description : In the given figure , two opposite angles of a parallelograms PQRS are (3x - 4)° and (56 - 3x)° . Find all the angles of given parallelogram . -Maths 9th

Last Answer : We know that opposite angles of a paralleloram are equal . ∴ ∠P = ∠R ⇒ 3x - 4 = 56 - 3x ⇒ 6x = 60 ⇒ x = 10 Thus, ∠P = ∠R = 3 10 - 4 = 26° Also, ∠P + ∠Q = 180° [ ... Hence, the four angles of the parallelogram PQRS are 26°, 154°,26° and 154°. We should care our earth to have good eco balance.

Check whether the graph of the equation y = 3x + 5 passes through the origin or not. -Maths 9th

Description : Check whether the graph of the equation y = 3x + 5 passes through the origin or not. -Maths 9th

Last Answer : Solution :-

For what value of p the point (p, 2) lies on the line 3x + y = 11? -Maths 9th

Description : For what value of p the point (p, 2) lies on the line 3x + y = 11? -Maths 9th

Last Answer : Solution :-

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

Last Answer : Solution :-

Give the geometric interpretations of 5x + 3 = 3x – 7 as an equation (i) in one variable (ii) in two variables. -Maths 9th

Description : Give the geometric interpretations of 5x + 3 = 3x – 7 as an equation (i) in one variable (ii) in two variables. -Maths 9th

Last Answer : Solution :-

Draw the graph of the equation 3x + 4y = 12 and find the co-ordinates of the points of intersection of the equation with the co-ordinate axes. -Maths 9th

Description : Draw the graph of the equation 3x + 4y = 12 and find the co-ordinates of the points of intersection of the equation with the co-ordinate axes. -Maths 9th

Last Answer : Solution :-