The roots of the equation `x^(2) + ax + b = 0` are `"______"`.

The roots of the equation `x^(2) + ax + b = 0` are `"______"`.
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The roots of the equation `x^(2) + ax + b = 0` are `"______"`.
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If the discriminant of the equation `ax^(2) + bx + c = 0` is greater than zero, then the roots are `"______"`.

Description : If the discriminant of the equation `ax^(2) + bx + c = 0` is greater than zero, then the roots are `"______"`.

Last Answer : If the discriminant of the equation `ax^(2) + bx + c = 0` is greater than zero, then the roots are `"______"`.

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

Last Answer : answer:

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.

Find the roots of quadratic equation `ax^(2) + (a-b + c) x - b +c = 0`.

Description : Find the roots of quadratic equation `ax^(2) + (a-b + c) x - b +c = 0`.

Last Answer : Find the roots of quadratic equation `ax^(2) + (a-b + c) x - b +c = 0`.

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 = \(\frac{7}{6}\).

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

Last Answer : answer:

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

Last Answer : answer:

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.

If the roots of the equation `ax^(2) + bx + c = 0` are in the ratio of `3 : 4`,

Description : If the roots of the equation `ax^(2) + bx + c = 0` are in the ratio of `3 : 4`,

Last Answer : If the roots of the equation `ax^(2) + bx + c = 0` are in the ratio of `3 : 4`,

The roots of a quadratic equation `ax^(2) + bx + c=0` are 1 and `c/a`, then `a + b = "_____"`.

Description : The roots of a quadratic equation `ax^(2) + bx + c=0` are 1 and `c/a`, then `a + b = "_____"`.

Last Answer : The roots of a quadratic equation `ax^(2) + bx + c=0` are 1 and `c/a`, then `a + b = "_____"`.

If the equation x2 minus ax plus 2b equals 0 has prime roots where a and b are positive integers then a minus b is equal to?

Description : If the equation x2 minus ax plus 2b equals 0 has prime roots where a and b are positive integers then a minus b is equal to?

Last Answer : I think you mean the roots are prime numbers.Let the two roots be primes p and qThen the equation factorises to (x - p)(x - q) = 0 which can beexpanded to give:x² - (p + q)x + pq = 0Which comparing ... = 2(It doesn't matter if the other prime is even (2) or not as itcancels out from a - b.)

If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`

Description : If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`

Last Answer : If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`

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 `"______"`.

If `-3` and 4 are the roots of the equation `(x+k) (x-4) =0` , then the value of k is `"______"`.

Description : If `-3` and 4 are the roots of the equation `(x+k) (x-4) =0` , then the value of k is `"______"`.

Last Answer : If `-3` and 4 are the roots of the equation `(x+k) (x-4) =0` , then the value of k is `"______"`.

Express the equation –x + 3y = -2/3 in the form of ax + by + c =0 and identify the values of a,b and c. -Maths 9th

Description : Express the equation –x + 3y = -2/3 in the form of ax + by + c =0 and identify the values of a,b and c. -Maths 9th

Last Answer : answer:

If one root of the equation ax^2 + x – 3 = 0 is –1, then what is the other root ? -Maths 9th

Description : If one root of the equation ax^2 + x – 3 = 0 is –1, then what is the other root ? -Maths 9th

Last Answer : answer:

If `x = 1` is a solution of the quadratic equation `ax^(2) - bx + c = 0`, then b is equal to `"_______"`.

Description : If `x = 1` is a solution of the quadratic equation `ax^(2) - bx + c = 0`, then b is equal to `"_______"`.

Last Answer : If `x = 1` is a solution of the quadratic equation `ax^(2) - bx + c = 0`, then b is equal to `"_______"`.

For the equation `2x^(2) - 3x + 5 = 0` sum of the roots is `"______"`.

Description : For the equation `2x^(2) - 3x + 5 = 0` sum of the roots is `"______"`.

Last Answer : For the equation `2x^(2) - 3x + 5 = 0` sum of the roots is `"______"`.

If the equation `3x^(2) - 2x-3 = 0`has roots `alpha`, and `beta` then `alpha.beta = "______"`.

Description : If the equation `3x^(2) - 2x-3 = 0`has roots `alpha`, and `beta` then `alpha.beta = "______"`.

Last Answer : If the equation `3x^(2) - 2x-3 = 0`has roots `alpha`, and `beta` then `alpha.beta = "______"`.

Find the equation of normals of the following curves at the given points: (i) Curve`y^(2)=4 ax" at point "(at^(2), 2at)`. (ii) Curve `y= e^(x)" at poi

Description : Find the equation of normals of the following curves at the given points: (i) Curve`y^(2)=4 ax" at point "(at^(2), 2at)`. (ii) Curve `y= e^(x)" at poi

Last Answer : Find the equation of normals of the following curves at the given points: (i) Curve`y^(2)=4 ax" at point "(at^( ... (2)-9y^(2) = 432` at point (6, 4).

The positive solutions of the equation ax + by + c = 0 always lie in the -Maths 9th

Description : The positive solutions of the equation ax + by + c = 0 always lie in the -Maths 9th

Last Answer : (a) We know that, if a line passes through the Ist quadrant, then all solution lying on the line in first quadrant must be positive because the coordinate of all points in the Ist quadrant are positive.

The positive solutions of the equation ax + by + c = 0 always lie in the -Maths 9th

Description : The positive solutions of the equation ax + by + c = 0 always lie in the -Maths 9th

Last Answer : (a) We know that, if a line passes through the Ist quadrant, then all solution lying on the line in first quadrant must be positive because the coordinate of all points in the Ist quadrant are positive.

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

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

Last Answer : Solution :-

If one root of the quadratic equation `ax^(2) + bx + c = 0` is `15 + 2sqrt(56)` and `a,b` and c are rational, then find the quadratic equation.

Description : If one root of the quadratic equation `ax^(2) + bx + c = 0` is `15 + 2sqrt(56)` and `a,b` and c are rational, then find the quadratic equation.

Last Answer : If one root of the quadratic equation `ax^(2) + bx + c = 0` is `15 + 2sqrt(56)` and `a,b` and c are rational, then find the quadratic equation.

If the roots of quadratic equation are equal , then the discriminant of the equation is `"______"`

Description : If the roots of quadratic equation are equal , then the discriminant of the equation is `"______"`

Last Answer : If the roots of quadratic equation are equal , then the discriminant of the equation is `"______"`

For the expression `ax^(2)+ 7x + 2` to be quadratic, the possible value of a are `"______"`.

Description : For the expression `ax^(2)+ 7x + 2` to be quadratic, the possible value of a are `"______"`.

Last Answer : For the expression `ax^(2)+ 7x + 2` to be quadratic, the possible value of a are `"______"`.

A body is projected from ground with speed 20 m/s making an angle of `45^(@)` with horizontal. The equation of path is `h = Ax-Bx^(2)`, where h is hei

Description : A body is projected from ground with speed 20 m/s making an angle of `45^(@)` with horizontal. The equation of path is `h = Ax-Bx^(2)`, where h is hei

Last Answer : A body is projected from ground with speed 20 m/s making an angle of `45^(@)` with horizontal. The equation of path ... B. 5 : 1 C. 1 : 40 D. 40 : 1

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

Last Answer : answer:

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

Last Answer : answer:

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

Last Answer : answer:

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

Last Answer : answer:

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

Last Answer : answer:

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

Last Answer : answer:

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.

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

Last Answer : answer:

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

Last Answer : answer:

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

Last Answer : answer:

If the roots of the equation (b – c)x2 + (c – a)x + (a – b) = 0 are equal, then prove that 2b = a + c. -Maths 10th

Description : If the roots of the equation (b – c)x2 + (c – a)x + (a – b) = 0 are equal, then prove that 2b = a + c. -Maths 10th

Last Answer : following is the equation of 2b = a+c =

If the roots ff the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 are equal, then prove that either a = 0 or a3 + b3 + c3 = 3abc -Maths 10th

Description : If the roots ff the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 are equal, then prove that either a = 0 or a3 + b3 + c3 = 3abc -Maths 10th

Last Answer : (c2 – ab) x2 + 2(bc - a2 ) x+ (b2 – ac) = 0 Comparing with Ax2 + Bx + C = 0 A = (c2 – ab), B = 2(bc - a2 ) and C = b2 – ac According to the question, B2 - 4AC = 0 Put the values in the above equation we get 4a(a3 + b3 + c3 -3abc) = 0 hence, a = 0 or a3 + b3 + c3 = 3ab

`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`

The quadratic equation `x^2-1088x+295680=0` has two positive integral roots whose greatest common divisor is 16. The least common multiple of the two

Description : The quadratic equation `x^2-1088x+295680=0` has two positive integral roots whose greatest common divisor is 16. The least common multiple of the two

Last Answer : The quadratic equation `x^2-1088x+295680=0` has two positive integral roots whose greatest common divisor is ... A. 18240 B. 18480 C. 18960 D. 19240

If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then the maximum value of the sum of the squares of

Description : If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then the maximum value of the sum of the squares of

Last Answer : If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then ... the roots is. A. 4 B. 3 C. `9//4` D. 2

Find the sum of the value (s) of a so that the equation (`x^(2) + 2ax + 2a + 3`) (`x^(2) + 2ax + 4a +5 `) = 0 has only 3 real distinct roots.

Description : Find the sum of the value (s) of a so that the equation (`x^(2) + 2ax + 2a + 3`) (`x^(2) + 2ax + 4a +5 `) = 0 has only 3 real distinct roots.

Last Answer : Find the sum of the value (s) of a so that the equation (`x^(2) + 2ax + 2a + 3`) (`x^(2) + 2ax + 4a +5 `) = 0 has only 3 real distinct roots.

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) = "_____"`.

If `k_(1)` and `k_(2)` are roots of `x^(2) - 5x - 24 = 0`, then find the quadratic equation whose roots are `-k_(1)` and `-k_(2)`.

Description : If `k_(1)` and `k_(2)` are roots of `x^(2) - 5x - 24 = 0`, then find the quadratic equation whose roots are `-k_(1)` and `-k_(2)`.

Last Answer : If `k_(1)` and `k_(2)` are roots of `x^(2) - 5x - 24 = 0`, then find the quadratic equation whose roots are `-k_(1)` and `-k_(2)`.

If `2alpha` and `3beta` are the roots of the equation `x^(2) + az +b = 0`, then find the equation whose roots are `a,b`.

Description : If `2alpha` and `3beta` are the roots of the equation `x^(2) + az +b = 0`, then find the equation whose roots are `a,b`.

Last Answer : If `2alpha` and `3beta` are the roots of the equation `x^(2) + az +b = 0`, then find the equation whose roots are `a,b`.

If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.

Description : If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.

Last Answer : If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.

If a, b are the roots of the equation `x^(2) - px +q = 0`, then find the equation which has `a/b` and `b/a` as its roots.

Description : If a, b are the roots of the equation `x^(2) - px +q = 0`, then find the equation which has `a/b` and `b/a` as its roots.

Last Answer : If a, b are the roots of the equation `x^(2) - px +q = 0`, then find the equation which has `a/b` and `b/a` as its roots.