Question

sum of the roots of a quadratic equation is double their product. Find k if equation is x^2-4kx+k+3=0

Answer 1

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

Answer 2

hope this will help u