Question

if alpha and beta are the zeros of the quadratic polynomial f(x) =k Square +4x+4 such that alpha square +beta square =24 find the value of k​

Answer 1

HEYA❣️

REFER TO THE ATTACHMENT ❣️

Answer 2

$\huge{SOLUTION:-}$

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According to the question,

α²+β² = 24

(α+β)² - 2(αβ)= 24

16/k² -8/k= 24

$\frac{16}{k^{2}}$ - $\frac{8}{k^{2}}$ = 24

$\frac{16 - 8k}{k^{2}}$= 24

16 - 8k = 24k²

24k² + 8k - 16 = 0

Dividing the eq. by 8

3k² + k - 4 = 0

3k² -3k + 4k - 4 = 0

3k ( k - 1) 4(k-1) = 0

Hence,

k = 1

Or

k = $\frac{-4}{3}$

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