Question

anyone please solve this question​

Answer 1

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

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$If \: \alpha \: and \: \beta\: are\: the\: zeroes \:of \:the\: polynomial\\ p(x) = 4t^2 - 5t - 1 ,\: find \:the\: value\: of \\ \alpha^2 \beta + \alpha \beta^2$

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

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

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

$\implies \alpha + \beta = \displaystyle{\frac{-(-5)}{4}}$

$\blue{\implies \alpha + \beta = \displaystyle{\frac{5}{4}}}$

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

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

$\blue{\implies \alpha \beta = \displaystyle{\frac{-1}{4}}}$

$\boxed{\red{\bold{Solving \: given \: equation:}}}$

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

$\implies \alpha \beta (\alpha + \beta)$

$\implies \displaystyle{\frac{-1}{4}} \left( \frac{5}{4} \right)$

$\green{\boxed{\implies \displaystyle{\frac{-5}{16}}}}$

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