Question

if alpha and beta are the zeroes of the quadratic polynomial f(x)= ax^2 + bx + c, then evaluate alpha^4 + beta^4​

Answer 1

Step-by-step explanation:

$if \: \alpha \: and \: \beta \: are \: zeroes \: of \: the \:$

$quadratic \: polynomial \: f(x) =a {x}^{2} +$

$bx + c$

$\alpha + \beta = - \frac{b}{a} \: and \: \alpha \beta = \frac{c}{a}$

${ \alpha }^{4} + { \beta }^{4} = > {( { \alpha }^{2} + { \beta }^{2})}^{2} - 2 { \alpha }^{2} { \beta }^{2} = >$

${( { \alpha }^{2} + { \beta }^{2})}^{2} - 2 {( \alpha \beta )}^{2} = >$

${( {( \alpha + \beta )}^{2} - 2 \alpha \beta ) }^{2} - 2 \frac{ {c}^{2} }{ {a}^{2} } = >$

${( \frac{ {b}^{2} }{ {a}^{2}} - 2 \frac{c}{a})}^{2} - 2 \frac{ {c}^{2} }{ {a}^{2}} = > (\frac{ {b}^{2} - 2ac }{ {a}^{2}})^2 - 2 \frac{ {c}^{2} }{{ a}^{2}}$

Hope it helps you.