Question

If alpha and beta are zeroes of polynomial 7x^2 + 8x + k ,such that alpha minus beta is 2 find value of k

Answer 1

Given,

α and β are zeroes of polynomial 7x² + 8x + k such that α - β = 2.

we have to find the value of k.

sum of zeroes = α + β = - coefficient of x/coefficient of x² = -8/7 ........(1)

product of zeroes = αβ = constant/coefficient of x² = k/7 ........(2)

using, (α - β)² = (α + β)² - 4αβ

⇒ (2)² = (-8/7)² - 4(k)/7 [from eq (1) and (2), ]

⇒4 = 64/49 - 28k/49

⇒4 × 49 = 64 - 28k

⇒196 - 64 = -28k

⇒132 = -28k

⇒k = -132/28 = -33/7

therefore value of k is -33/7