if alpha and beta are zeros of the polynomial x^2+7x+3, find a quadratic polynomial whose zeroes are alpha/beta and beta/alpha
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Answer:
Given that,
α,β are the zeroes of the polynomial p(x)=2x2−7x+3
Sum of zeroes (α+β)=a−b=2−(−7)=27
Product of zeroes αβ=ac=23
∴α2+β2=(α+β)2−2αβ
=(27)2−2(23)
=449−41
=437
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