Question

if a and b are the roots of equation

Answer 1

$hey \: mate \: here \: is \: your \: answer...$


$the \: given \: polynomial \: is \: -$
${x}^{2} - 6x + 2 = 0$

$\alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 6)}{1} = \frac{6}{1} = 6$


$\alpha \beta = \frac{c}{a} = \frac{2}{1} = 2$


$\alpha {}^{4} \beta {}^{3} + \alpha {}^{3} \beta {}^{4} = \alpha {}^{3} \beta {}^{3} ( \alpha + \beta )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (\alpha \beta ) {}^{3} ( \alpha + \beta )$


$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2) {}^{3} (6)$


$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (8)(6)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 48$





$\: the \: value \: of \: { \alpha }^{4} \beta {}^{3} + \alpha {}^{3} \beta {}^{4} is \: 48$






$hope \: it \: helps.....$