Question

ifα,β are the zeroes of the polynomial ax^2 +bx+c,then (α^2+β^2)=
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Answer 1

✰ Hello

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➥Ur answer :

$\alpha \: and \: \beta \: are \: the \: Zeroes \: of \: the \: Polynomial \: a {x}^{2} + bx + c = 0 \\ then \: \alpha + \beta \: = \frac{ - b}{ \: a } \: \: \: and \: \: \alpha \beta = \frac{c}{a} \\ {( \alpha + \beta )}^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta \\ \frac{ {b}^{2} }{ {a}^{2} } = { \alpha }^{2} + { \beta }^{2} + \frac{2c}{a} \\ { \alpha }^{2} + { \beta }^{2} = \frac{ {b}^{2} }{ {a}^{2} } - \frac{2c}{a} \\ { \alpha }^{2} + { \beta }^{2} = \frac{ {b}^{2} - 2ac}{ {a}^{2} }$

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