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Quadratic Equations

MHT-CET Maths. Try each one first, then open its answer.

Top 6 MHT-CET 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

    Asked 2 times: 9 May 2024 S2*, 14 May 2024 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    132
    The equation x3+x−1=0x^3+x-1=0 has

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  2. Question 2

    Asked once: 18 Apr 2026 S2

    51
    The difference between the roots of the equation x2+2x+4=0x^2 + 2x + 4 = 0 is …\ldots (where i=−1i = \sqrt{-1})

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  3. Question 3

    Asked once: 13 Apr 2026 S2

    51
    The quadratic polynomial p(x)p(x) has roots 11 and α\alpha, while quadratic polynomial q(x)q(x) has roots 11 and β\beta. Let α\alpha and β\beta be the roots of r(x)=p(x)+q(x)r(x) = p(x) + q(x). Then lim⁡x→∞[p(x)−q(x)]=\lim_{x \to \infty}\left[\sqrt{p(x)} - \sqrt{q(x)}\right] =

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  4. Question 4

    Asked once: 20 Apr 2025 S2

    141
    If f(x)=2x3+mx2−13x+nf(x) = 2x^{3}+mx^{2}- 13x+n and 2,3 are the roots of the equation f(x)=0f(x) = 0 then the value of 4m+5n4m+ 5n is

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  5. Question 5

    Asked once: 19 Apr 2025 S2

    148
    The value of 'a' so that the sum of squares of the roots of the equation x2−(a−2)x−a+1=0x^{2}- (a- 2)x-a+ 1 = 0 assumes the least value is

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  6. Question 6

    Asked once: 9 May 2023 S2

    104
    Let α,β\alpha, \beta be the roots of the equation x2−px+r=0x^2 - px + r = 0 and α2,2β\frac{\alpha}{2}, 2\beta be the roots of the equation x2−qx+r=0x^2 - qx + r = 0. Then the value of rr is

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