If alpha, beta are the roots of the quadratic | vedclass

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(A) Given the quadratic equation $x^{2}-8x+k=0$.Since $\alpha$ and $\beta$ are the roots of the equation,by the relationship between roots and coeffic

Vedclass · Accepted Answer

$12$

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(A) Given the quadratic equation $x^{2}-8x+k=0$.Since $\alpha$ and $\beta$ are the roots of the equation,by the relationship between roots and coefficients:Sum of roots $\alpha+\beta = -(-8)/1 = 8$.Product of roots $\alpha\beta = k/1 = k$.We are given the condition $\alpha^{2}+\beta^{2}=40$.Using the identity $\alpha^{2}+\beta^{2} = (\alpha+\beta)^{2} - 2\alpha\beta$:$40 = (8)^{2} - 2k$.$40 = 64 - 2k$.$2k = 64 - 40$.$2k = 24$.$k = 12$.

If $\alpha, \beta$ are the roots of the quadratic equation $x^{2}-8x+k=0$,find the value of $k$ such that $\alpha^{2}+\beta^{2}=40$.

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