Question

If alpha,beta are the roots of x²-bx+c =0 then alpha*beta³ +alpha³*beta

Answer 1

${x}^{2} - bx + c = 0 \\ \alpha + \beta = b \\ \alpha \beta = c \\ \\ \alpha { \beta }^{ 3} + { \alpha }^{3} \beta = \alpha \beta ( { \alpha }^{2} + { \beta }^{2} )$
Now consider this
$\alpha + \beta = b \\ { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta = {b}^{2} \\ { \alpha }^{2} + { \beta }^{2} + 2c = {b}^{2} \\ { \alpha }^{2} + { \beta }^{2} = {b}^{2} - 2c$
Now substitute this in the required equation to get the answer.
$\alpha { \beta }^{ 3} + { \alpha }^{3} \beta = \alpha \beta ( { \alpha }^{2} + { \beta }^{2} ) \\ = c( {b}^{2} - 2c)$
Mark it as the brainliest answer.