if alpha beta gamma are the zeros of the polynomial ax3+bx2+cx+d.find the value of alpha square beta square and gamma square.

We have,fx=ax3+bx2+cx+dα, β and γ are the roots of fxα+β+γ=-baαβ+βγ+αγ=caAndαβγ=-daNow,α+β+γ2=α2+β2+γ2+2αβ+βγ+αγ-ba2=α2+β2+γ2+2caα2+β2+γ2=b2a2-2caα2+β2+γ2=b2-2aca2

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