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Question

Ifα,βbetherootsoftheequationax2+bx+c=0thenthevalueofaα2bα+c+aβ2bβ+cisequalto

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Solution

Here,αandβarerootsoftheequationax2+bx+c=0α+β=ba&αβ=caaα+aβ=b&aαβ=caα2bα+c+aβ2bβ+c=aα2bα+aαβ+aβ2bβ+aαβ=aα2α(b+aβ)+aβ2β(b+aα)=aα(b+aβ)+aβ(b+aα)=(b+αβ)(b+aβ)(b+aα)(b+aα)=11=2

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