Question

If alpha and beta are the zeroes of the polynomial kx^2 + 4x +4 and (alpha*beta)^2 - 2*alpha*beta= 24, then find the value of k .

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Answer 1

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Answer 2

Answer:

k=2/3 or -1

Step-by-step explanation:

α and β are the zeroes of polynomial kx² + 4x + 4

a = k

-b = -4

c = 4

α + β = -b/a = -4/k

αβ = c/a = 4/k

Given => α² + β² = 24

=> (α + β)² - 2αβ = 24

=> (-4/k)² - 2×4/k = 24

=> 16/k² - 8/k = 24

=> 16 - 8k = 24k²

=> 24k² + 8k - 16 = 0

=> 3k² + k - 2 = 0

=> 3k² + 3k - 2k - 2 = 0

=> 3k(k + 1) - 2(k + 1) = 0

=> (3k - 2)(k + 1) = 0

=> k = 2/3 or -1