Question

16) Sum of the roots of a quadratic equation is double their product find k if equation is x² - 4kx+k+3=0
1) 3
2) -3
3) 2
4) 1

Answer 1

Answer:

Let α and β are the roots of quadratic equation x² - 4kx + k + 3 = 0

∴sum of roots = - coefficient of x²/coefficient of x

α + β = -(-4k)/1 = 4k

Product of roots = constant/coefficient of x²

αβ = (k + 3)/1 = (k + 3)

A/C to question,

sum of roots = 2 × product of roots

(α + β ) = 2αβ

⇒4k = 2(k + 3)

⇒ 4k = 2k + 6

⇒ 4k - 2k = 6

⇒ 2k = 6

⇒ k = 3

Hence, answer is k = 3