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Quadratic Equations

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 6 times: CDS 1 2017, CDS 2 2021, CDS 2 2022, CDS 1 2023, CDS 2 2024, CDS 2 2026. This one: CDS 2 2026 See all 6 of this type

    16
    If α\alpha and β\beta are the roots of the equation 2x2−2(n+1)x+(n2+n+1)=02x^2 - 2(n + 1)x + (n^2 + n + 1) = 0, then what is (2α3+2β3)(2\alpha^3 + 2\beta^3) equal to ?

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  2. Question 2

    This type asked 5 times: CDS 2 2017, CDS 1 2021, CDS 1 2023, CDS 2 2024, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    13
    If 5 is a root of the equation x2+px−55=0x^2 + px - 55 = 0 and the quadratic equation x2+px+k=0x^2 + px + k = 0 has equal roots, then what is the value of k ?

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  3. Question 3

    This type asked 5 times: CDS 2 2019, CDS 1 2020, CDS 1 2022, CDS 1 2023, CDS 2 2025. This one: CDS 2 2025 See all 5 of this type

    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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  4. Question 4

    This type asked 4 times: CDS 2 2018, CDS 1 2019, CDS 2 2024, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    1
    A real number M is squared to give the value N. What is the minimum value of (M+N)(M + N) ?

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  5. Question 5

    This type asked 4 times: CDS 2 2016, CDS 1 2019, CDS 1 2022, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    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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  6. Question 6

    This type asked 4 times: CDS 2 2020, CDS 2 2021, CDS 2 2022, CDS 1 2024. This one: CDS 1 2024 See all 4 of this type

    14
    What is the greatest value of k for which 2x2−4x+k=02x^2 - 4x + k = 0 has real roots ?

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  7. Question 7

    This type asked 3 times: CDS 1 2023, CDS 2 2023, CDS 2 2025. This one: CDS 2 2025 See all 3 of this type

    25
    If (a−b2)x2−(a+b2)x+b=0\left(\frac{a-b}{2}\right)x^2-\left(\frac{a+b}{2}\right)x+b=0, then what are the roots of this equation?

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  8. Question 8

    This type asked 3 times: CDS 2 2017, CDS 1 2019, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type

    80
    The equations x2+px+q=0x^2 + px + q = 0 and x2+qx+p=0x^2 + qx + p = 0 (p≠q)(p \ne q) have a common root. What is the value of (p+q)(p + q) ?

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  9. Question 9

    This type asked 3 times: CDS 1 2017, CDS 2 2017, CDS 1 2022. This one: CDS 1 2022 See all 3 of this type

    38
    What is the condition that the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0 are in the ratio c:1c : 1 ?

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  10. Question 10

    Asked 2 times: CDS 1 2019*, CDS 2 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    1
    A real number xx is such that the sum of the number and four times its square is the least. What is that number ?

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