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(ap/f α and pare the zeroes ofthe quadratic polynomial f(x)-kx2 +4x + 4 such that α, p, 24, find the.ue of k |
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Answer» Solution :- α and β are the zeros of the given polynomial Kx² + 4x + 4 = 0so, product of zeros = αβ = constant/coefficient of x² = 4/Ksum of zeros = α + β = -coefficient of x/Coefficient of x² = -4/k Now, α² + β² = 24 ⇒(α + β)² - 2αβ = 24 ⇒(-4/k)² - 2(4/k) = 24 ⇒16/K² - 8/k = 24 ⇒ 2 - k = 3k² ⇒3k² + k -2 = 0 ⇒ 3k² + 6k - k - 2 = 0⇒3k(k + 2) - 1(k +2) = 0⇒(3k -1)(k +2) = 0 Hence, k = 1/3 and -2 |
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