Question

if α,β are the roots of the quadratic equation x2-2x-1=0,find the value of α2β+β2α.

Answer 1

eq. is
${x}^{2} - 2x - 1 = 0$

$\alpha + \beta = \frac{ - b}{a}$
$\alpha + \beta = 2 \: \: - (i)$
$\alpha .\beta = \frac{c}{a}$
$\alpha . \beta = - 1 \: \: - (ii)$
now

${ \alpha }^{2} \beta + { \beta }^{2} \alpha$
$= \alpha \beta ( \alpha + \beta )$
$= ( - 1)(2)$
$= - 2$
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