Advertisements
Advertisements
Question
Form the quadratic equation if its roots are –3 and 4.
Advertisements
Solution
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
RELATED QUESTIONS
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
Solve the following quadratic equation using formula method only
`3"x"^2 + 2 sqrt 5x - 5 = 0 `
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Solve the following quadratic equation using formula method only
25x2 + 30x + 7 = 0
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0.
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
Which of the following equations has the sum of its roots as 3?
Every quadratic equation has at least two roots.
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least is ______.
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
