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Sum of squares of the zeros from the coefficients

This type of question, asked 2 times: CDS 2 2018, CDS 1 2024. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    50
    If α\alpha, β\beta and γ\gamma are the zeros of the polynomial f(x)=ax3+bx2+cx+df(x) = ax^3 + bx^2 + cx + d, then α2+β2+γ2\alpha^2 + \beta^2 + \gamma^2 is equal to

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  2. Question 2

    CDS 1 2024

    8
    If 2 is a zero of the polynomial p(x)=x3+3x2−6x−ap(x) = x^3 + 3x^2 - 6x - a, then what is the sum of the squares of the other zeros of the polynomial ?

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