Advertisements
Advertisements
प्रश्न
Form the quadratic equation if its roots are –3 and 4.
Advertisements
उत्तर
Given that
α = -3, β = 4
∴ α + β = (-3) + 4 = 1
α.β = -3 x 4 = -12
∴ The quadratic equation which roots are α and β is
x2 - (α+β)x + αβ = 0
∴ x2 - x - 12 = 0
APPEARS IN
संबंधित प्रश्न
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.
If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
