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Question

If α,β are the roots of ax2+bx+c=0,(a0) then find the values of α2β+αβ2

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Solution

We have,
value of α2+β2
The polynomial is ax2+bx+c whose zeroes are α and β
Thus sum of the zeroes =α+β=ba
The product of the zeroes =α×β=ca
α2+β2=(α+β)2=2αβ
=(ba)2=2×ca
=b2a22ca
=b22aca2
Hence, this is answer.

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