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Question

If α and β are the zeros of the quadratic polynomial f(x)=ax2+bx+c, then evaluate :
1aα+β+1aβ+α

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Solution

Given,

f(x)=ax2+bx+c

α+β=ba

αβ=ca

1aα+b+1aβ+b

=aβ+b+aα+b(aα+b)(aβ+b)

=a(α+β)+2ba2αβ+ab(α+β)+b2

=a(ba)+2ba2(ca)+ab(ba)+b2

=b+2bacb2+b2=bac

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