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x^2 + px + q = 0 has roots p and q: find p, q and expressions in them

This type of question, asked 4 times: CDS 2 2016, CDS 1 2019, CDS 1 2022, CDS 1 2025. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    20
    If pp and qq are the roots of x2+px+q=0x^2 + px + q = 0, then which one of the following is correct ?

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  2. Question 2

    CDS 1 2019

    89
    The equation x2+px+q=0x^2 + px + q = 0 has roots equal to pp and qq where q≠0q \ne 0. What are the values of pp and qq respectively ?

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  3. Question 3

    CDS 1 2022

    31
    If α\alpha and β\beta are the roots of the quadratic equation x2+αx+β=0x^2 + \alpha x + \beta = 0, where β≠0\beta \ne 0, then what is the value of α−β\alpha - \beta ?

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  4. Question 4

    CDS 1 2025

    79
    If p (≠0)p\,(\ne 0) and q (≠0)q\,(\ne 0) are the roots of the equation x2+px+q=0x^2 + px + q = 0, then what is p2+q2p^2 + q^2 equal to ?

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