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

The equation whose roots are twice the roots of the equation x^2 – 3x + 3 = 0 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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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

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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)

Which one of the following is the equation whose roots are respectively three times the roots of the equation ax^2 + bx + c = 0 ? -Maths 9th

Description : Which one of the following is the equation whose roots are respectively three times the roots of the equation ax^2 + bx + c = 0 ? -Maths 9th

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The quadratic equation whose roots are three times the roots of 3ax^2 + 3bx + c = 0 is -Maths 9th

Description : The quadratic equation whose roots are three times the roots of 3ax^2 + 3bx + c = 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).

A quadratic equation whose roots are 2 moe than the roots of the quadratic equation `2x^(2) +3x + 5 = 0`, can be obtained by substituting `"_____"` fo

Description : A quadratic equation whose roots are 2 moe than the roots of the quadratic equation `2x^(2) +3x + 5 = 0`, can be obtained by substituting `"_____"` fo

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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

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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

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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.

If one of the roots of the equation x^2 + ax + 3 = 0 is 3 and one of the roots of the equation x2 + ax + b = 0 is three -Maths 9th

Description : If one of the roots of the equation x^2 + ax + 3 = 0 is 3 and one of the roots of the equation x2 + ax + b = 0 is three -Maths 9th

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If the difference in the roots of the equation x^2 – px + q = 0 is unity, then which one of the following is correct ? -Maths 9th

Description : If the difference in the roots of the equation x^2 – px + q = 0 is unity, then which one of the following is correct ? -Maths 9th

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If the roots of the equation x^2 – 2ax + a^2 + a – 3 = 0 are real and less than 3, then which one of the following is correct ? -Maths 9th

Description : If the roots of the equation x^2 – 2ax + a^2 + a – 3 = 0 are real and less than 3, then which one of the following is correct ? -Maths 9th

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If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

Description : If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

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What are the roots of the equation 4^x – 3.2^(x + 2) + 32 = 0 ? -Maths 9th

Description : What are the roots of the equation 4^x – 3.2^(x + 2) + 32 = 0 ? -Maths 9th

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What are the roots of the quadratic equation a^2 b^2 x^2 – (a^2 + b^2)x + 1 = 0 ? -Maths 9th

Description : What are the roots of the quadratic equation a^2 b^2 x^2 – (a^2 + b^2)x + 1 = 0 ? -Maths 9th

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If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

Description : If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

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If the roots of the equation a(b – c) x^2 + b(c – a)x + c(a – b) = 0 are equal, then a, b, c are in : -Maths 9th

Description : If the roots of the equation a(b – c) x^2 + b(c – a)x + c(a – b) = 0 are equal, then a, b, c are in : -Maths 9th

Last Answer : As we know that for the quadratic equation ax2+bx+c=0, roots will be equal if D=B2−4AC=0 Therefore, for the equation, a(b−c)x2+b(c−a)x+c(a−b)=0 A=a(b−c),B=b(c−a),C=c(a−b) D=0 B2−4AC=0 (b(c−a))2−4(a(b−c))(c(a−b))=0 ⇒ab+bc=2ac Hence a,b and c are in HP.

Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Description : Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Last Answer : Let αα and ββ be the roots of the quadratic equation x2+px+q=0x2+px+q=0 Given that, A starts with a wrong value of p and obtains the roots as 2 and 6. But this time q is correct. i.e., a product of roots ... 1 Now, from Eqs. (ii) and (iii), we get α=−3 and β=−4α=−3 and β=−4 which are correct roots.

If the roots of the equation x^3 – ax^2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ? -Maths 9th

Description : If the roots of the equation x^3 – ax^2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ? -Maths 9th

Last Answer : Let the roots of the equation x3 – ax2 + bx – c = 0 be (α – 1), α, (α + 1) ∴ S2 = (α – 1)α + α(α + 1) + (α + 1) ( ... ; 1 = b ⇒ 3α2 – 1 = b ∴ Minimum value of b = – 1, when α = 0.

If the equation (a^2 + b^2) x^2 – 2 (ac + bd)x + (c^2 + d^2) = 0 has equal roots, then which one of the following is correct ? -Maths 9th

Description : If the equation (a^2 + b^2) x^2 – 2 (ac + bd)x + (c^2 + d^2) = 0 has equal roots, then which one of the following is correct ? -Maths 9th

Last Answer : The given quadratic equation is (a2 + b2)x2 − 2(ac + bd)x + (c2 + d2) = 0. If the roots of given quadratic equation are equal, then its discriminant is zero.

Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

Description : Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

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Twice the number of marbles with Aman exceeds thrice the number of marbles with Vinay by 12. Assume the number of marbles with Aman and Vinay as x and y respectively .Express the statement in the form of a linear equation in two variables. -Maths 9th

Description : Twice the number of marbles with Aman exceeds thrice the number of marbles with Vinay by 12. Assume the number of marbles with Aman and Vinay as x and y respectively .Express the statement in the form of a linear equation in two variables. -Maths 9th

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The length of a rectangular piece of fabric is twice its width . identify the geometrical representation of this situation when represented as an equation in two variables. Width and length be represented as x and y respectively . -Maths 9th

Description : The length of a rectangular piece of fabric is twice its width . identify the geometrical representation of this situation when represented as an equation in two variables. Width and length be represented as x and y respectively . -Maths 9th

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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.

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

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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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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

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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

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What is the equation of the line joining the origin with the point of intersection of the lines 4x + 3y = 12 and 3x + 4y = 12 ? -Maths 9th

Description : What is the equation of the line joining the origin with the point of intersection of the lines 4x + 3y = 12 and 3x + 4y = 12 ? -Maths 9th

Last Answer : (b) (5, 6)Let the foot of the perpendicular be M(x1, y1) Slope of line AB, i.e., y = -x + 11 = -1 Slope of line PM = \(rac{y_1-3}{x_1-2}\)Now, PM ⊥ AB⇒ \(\bigg(rac{y_1-3}{x_1-2}\bigg)\) x - ... get 2x1 = 10 ⇒ x1 = 5 Putting x1 in (ii), we get y1 = 6. ∴ Required foot of the perpendicular M is (5, 6).

What are the roots of the equation (a + b + x) ^(–1) = a^(–1) + b^(–1) + x^(–1) ? -Maths 9th

Description : What are the roots of the equation (a + b + x) ^(–1) = a^(–1) + b^(–1) + x^(–1) ? -Maths 9th

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What are the roots of the equation log10 (x^2 – 6x + 45) = 2? -Maths 9th

Description : What are the roots of the equation log10 (x^2 – 6x + 45) = 2? -Maths 9th

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The sum of the roots of the equation (1/(x+a))+(1/(x+b))=1/c is zero. What is the product of the roots of the equation ? -Maths 9th

Description : The sum of the roots of the equation (1/(x+a))+(1/(x+b))=1/c is zero. What is the product of the roots of the equation ? -Maths 9th

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In quadratic equation ax^2 + bx + c = 0 , Identities the sum and product of Roots? -Maths 9th

Description : In quadratic equation ax^2 + bx + c = 0 , Identities the sum and product of Roots? -Maths 9th

Last Answer : If the two roots of the quadratic equation ax2 + bx + c = 0 obtained by the quadratic formula be denoted by a and b, then we have α = \(\frac{-b+\sqrt{b^2-4ac}}{2a},\) β = \(\frac{-b-\sqrt{b^2-4ac}}{2a}\) ∴ Sum of roots ... then α + β = - (- \(\frac{5}{6}\)) = \(\frac{5}{6}\), ab = \(\frac{7}{6}\).

What is the ratio of sum of squares of roots to the product of the roots of the equation 7x^2 + 12x + 18 = 0? -Maths 9th

Description : What is the ratio of sum of squares of roots to the product of the roots of the equation 7x^2 + 12x + 18 = 0? -Maths 9th

Last Answer : Let α, β be the roots of the equation 7x2 + 12x + 18 = 0. ∴ Required ratio = α2 + β2 : αβ = ​​−10849187 = −67 = – 6 : 7.

For what value of m the ratio of the roots of the equation 12x^2 – mx + 5 = 0 is 3 : 2 ? -Maths 9th

Description : For what value of m the ratio of the roots of the equation 12x^2 – mx + 5 = 0 is 3 : 2 ? -Maths 9th

Last Answer : Given equation: 12x2+mx+5=0 The roots are in ratio 3:2 Hence,let roots of the equations are 3α and 2α. Applying condition for sum and product of the roots, 3α+2α=−12m​ and 3α×2α=125​⇒α2=725​⇒α=±62​5​​And m=−60α ⇒m=±510​Hence, A is the correct option.

If the roots of the equation ax^2 + bx + c = 0 are equal in magnitude but opposite in sign, then which one of the following is correct ? -Maths 9th

Description : If the roots of the equation ax^2 + bx + c = 0 are equal in magnitude but opposite in sign, then which one of the following is correct ? -Maths 9th

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For what value of k will the roots of the equation kx^2 – 5x + 6 = 0 be in the ratio 2 : 3 ? -Maths 9th

Description : For what value of k will the roots of the equation kx^2 – 5x + 6 = 0 be in the ratio 2 : 3 ? -Maths 9th

Last Answer : (b) 1 Let the roots of the equation kx2 - 5x + 6 = 0 be α and β. Then, α + β = \(\frac{5}{k}\) ...(i) αβ = \(\frac{6}{k}\) ...(ii) Given \(\ ... frac{9}{k}\) ⇒ 9k2 - 9k = 0 k(k - 1) = 0 ⇒ k = 0 or 1 But k = 0 does not satisfy the condition, so k = 1.

If p, q, r are positive and are in A.P., the roots of quadratic equation px^2 + qx + r = 0 are real for : -Maths 9th

Description : If p, q, r are positive and are in A.P., the roots of quadratic equation px^2 + qx + r = 0 are real for : -Maths 9th

Last Answer : Given p,q,r are in A.P. then q=2p+r​.....(1). Now px2+qx+r=0 will have real root then q2−4pr≥0. or, 4(p+r)2​−4pr≥0 or, p2+r2−14pr≥0 or, r2−14rp+49p2≥48p2 or, (r−7p)2≥(43​p)2 or, (pr​−7)2≥(43​)2 [ Since p=0 for the given equation to be quadratic] or, ∣∣∣∣∣​pr​−7∣∣∣∣∣​≥43​.

If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th

Description : If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th

Last Answer : Given equation: ax2+bx+c=0 Let α and β be the roots of given quadratic equation Sum of the roots i.e. α+β=a−b Product of roots i.e. αβ=ac It is given that, Sum of the roots = Sum of squares of the roots i ... )2−2αβ i.e. a−b =(a−b )2−a2c i.e. −ab=b2−2ac i.e. ab+b2=2ac Hence, C is the correct option.

`x_1 ,x_2` are the `x^2-3x+A= 0; x_3 , x_4` are roots of the equation `x^2-12x + B =0` of the equation `x_1 ,x_2 ,x_3 , x_4` form in increasing `GP`.,

Description : `x_1 ,x_2` are the `x^2-3x+A= 0; x_3 , x_4` are roots of the equation `x^2-12x + B =0` of the equation `x_1 ,x_2 ,x_3 , x_4` form in increasing `GP`.,

Last Answer : `x_1 ,x_2` are the `x^2-3x+A= 0; x_3 , x_4` are roots of the equation `x^2-12x + B =0` of the equation `x_1 ... x_(1) + x_(3) =5` D. `x_(2)+x_(4)=10`

If `alpha` and `beta` are the roots of the quadratic equation `x^(2) + 3x - 4 = 0`, then `alpha^(-1) + beta^(-1) = "_____"`.

Description : If `alpha` and `beta` are the roots of the quadratic equation `x^(2) + 3x - 4 = 0`, then `alpha^(-1) + beta^(-1) = "_____"`.

Last Answer : If `alpha` and `beta` are the roots of the quadratic equation `x^(2) + 3x - 4 = 0`, then `alpha^(-1) + beta^(-1) = "_____"`.

The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.

Description : The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.

Last Answer : The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.

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

Description : 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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In a public examination , Raghav scored twice twice Sunitha’s score. If r and s represent the scores of Raghav and Sunitha respectively , Write a linear equation in r and s representing the above situation ? -Maths 9th

Description : In a public examination , Raghav scored twice twice Sunitha’s score. If r and s represent the scores of Raghav and Sunitha respectively , Write a linear equation in r and s representing the above situation ? -Maths 9th

Last Answer : Let raghav and sunita score be r and S respectively. Sunita score=2times raghav score Therefore, s=2r

The sum of twice the age of Ram and one-third the age of Shyam is 62 years. Express the statement as a linear equation in two variables. -Maths 9th

Description : The sum of twice the age of Ram and one-third the age of Shyam is 62 years. Express the statement as a linear equation in two variables. -Maths 9th

Last Answer : Let Ram's age be x and Shyam's age be y. Then, 2x+1/3y=62

The diagonal of a square A is (a + b). The diagonal of a square whose area is twice the area of square A is. -Maths 9th

Description : The diagonal of a square A is (a + b). The diagonal of a square whose area is twice the area of square A is. -Maths 9th

Last Answer : (c) (a+b)√2.Area of new square = 2 (Area of the square A)= \(2 imesrac{ ext{(diagonal)}^2}{2}=2 imesrac{(a+b)^2}{2}= (a+b)^2\)∴ Each side of new square = (a + b) ⇒ Diagonal of new square = side √2 = (a+b)√2.

Explain Nature of Roots of a quadratic equation. -Maths 9th

Description : Explain Nature of Roots of a quadratic equation. -Maths 9th

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If the sum as well as the product of roots of a quadratic equation is 9, then the equation is: -Maths 9th

Description : If the sum as well as the product of roots of a quadratic equation is 9, then the equation is: -Maths 9th

Last Answer : answer: