Question

anyone please do it ​

Answer 1

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$If\: the \:sum \:of \:zeroes\: of\; the\: squares\: of \\ the\: polynomial\: f(x) = x^2 -8x +k \:is \\ 40 , \:find \:the\: value \:of \:k.$

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$\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Answer}}}}}{\bigstar}$

$\purple{Let \: zeroes \: are \; \alpha \: , \beta}$

$\boxed{\red{\bold{Sum \: of \: zeroes:}}}$

$\implies \alpha + \beta = \displaystyle{\frac{-b}{a}}$

$\blue{\implies \alpha + \beta = \displaystyle{\frac{-(-8)}{1}}}$

$\blue{\implies \alpha +\beta = 8}$

$\boxed{\red{\bold{Product \: of \: zeroes:}}}$

$\implies \alpha \beta = \displaystyle{\frac{c}{a}}$

$\implies \alpha \beta = \displaystyle{\frac{k}{1}}$

$\blue{\implies \alpha \beta = k}$

$\boxed{\red{\bold{Given \: relation}}}$

$\purple{\implies \alpha ^2 + \beta ^2=40}$

$\green{\implies \alpha ^2 + \beta ^2 + 2 \alpha \beta - 2 \alpha \beta = 40 }$

$\green{\implies (\alpha + \beta ) ^2-2 \alpha \beta = 40}$

$\green{\implies 8^2 - 2(k) = 40}$

$\green{\implies 64 - 2k = 40}$

$\green{\implies 2k = 24}$

$\green{\boxed{\implies k = 12}}$

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