Question

If α and β are zeroes of x² - (k - 6)x + 2(2k - 1) find the value of k if α + β = (1/2)αβ.

Answer 1

α, β are the zeroes of x² − (k - 6)x + 2(2k − 1)

i.e, α + β = k - 6 (Sum of roots of quadratic)

and αβ = 2(2k − 1) (Product of roots)

According to question,

α + β = \(\frac 12\)αβ

⇒ k - 6 = \(\frac{2(2k - 1)}{2} \)

⇒ k - 6 = 2k -1

⇒ 2k - k = -6 + 1

⇒ k = -5

Answer 2

Given, α, β are the zeroes of polynomial

x² - (k - 6)x + 2(2k - 1)

Hence the value of k = -5