Question

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if α,β are zeros of a quadratic polynomial 2x²+5x²+k, find the value of k, such that (α+β)²-αβ=24

Answer 1

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Answer 2

$\alpha + \beta = - \frac{b}{a} \\ \alpha \beta = \frac{c}{a}$
Where a=2
b=5
c=k
${( \alpha + \beta )}^{2} - \alpha \beta \\ = { \frac{ (- b)}{(a)} }^{2} - ( \frac{c}{a} )$
$= \frac{25}{4} - \frac{k}{2} \\ \frac{25 - 2k}{4} = 24 \\ 25 - 2k = 96 \\ 2k = 25 - 96 \\ = - 71$
k=-71/2