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Question

If α,β are zeroes of the quadratic polynomial ax2+bx+c then find the value of α2β2.

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Solution

ax2+bx+c=0
α+β=baαβ=ca
(α+β)2=b2a2
(αβ)2=(α+β)24αβ
=b2a24ca=b24aca2
αβ=b24aca
α2β2=(α+β)(αβ)=ba(b24aca)
=bb24aca2

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