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Difference of the roots given: use (a - b)^2 = (a + b)^2 - 4ab

This type of question, asked 5 times: CDS 2 2019, CDS 1 2020, CDS 1 2022, CDS 1 2023, CDS 2 2025. All 5 questions below, oldest first.

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  1. Question 1

    CDS 2 2019

    48
    If p and q are the roots of the equation x2−15x+r=0x^2 - 15x + r = 0 and p−q=1p - q = 1, then what is the value of r ?

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  2. Question 2

    CDS 1 2020

    12
    If α\alpha and β\beta are the roots of the quadratic equation x2+kx−15=0x^{2} + kx - 15 = 0 such that α−β=8\alpha - \beta = 8, then what is the positive value of kk ?

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  3. Question 3

    CDS 1 2022

    36
    If the sum of the roots of the equation x2−k2x+30kx−161x−64=0x^2 - k^2 x + 30kx - 161x - 64 = 0 is zero, then what is the difference of the roots?

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  4. Question 4

    CDS 1 2023

    4
    If the roots of the equation x2−bx+c=5x^2 - bx + c = 5 differ by 5, then which one of the following is correct?

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  5. Question 5

    CDS 2 2025

    57
    If one root of the equation 2x2−5px+2p2=02x^2 - 5px + 2p^2 = 0 exceeds the other by 4, then what is the value of pp ?

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