If α and β are the zeroes of the polynomial p(x) = kx² + 3x +2 , then 1/α + 1/β = ---------------
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According to the question,
α and β are the zeroes of polynomial kx² + 4x + 4
a = k
-b = -4c = 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
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