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Rolle's theorem holds for a cubic on [1, 3] with c = 2 + 1/sqrt3: find its coefficients

The same question, asked 4 times: 2 May 2023 S1, 13 May 2024 S2, 11 Apr 2026 S2*, 12 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    138
    If Rolle's theorem holds for the function f(x)=x3+bx2+ax+5f(x) = x^3 + bx^2 + ax + 5 on [1,3][1,3] with c=2+13c = 2 + \dfrac{1}{\sqrt{3}}, then the values of aa and bb respectively are

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  2. Question 2

    13 May 2024 S2

    108
    If Rolle's theorem holds for the function f(x)=x3+bx2+ax+5f(x)=x^3+bx^2+ax+5 on [1,3][1,3] with c=2+13c=2+\frac{1}{\sqrt{3}}, then the values of aa and bb respectively are

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  3. Question 3

    11 Apr 2026 S2

    74
    If the function f(x)=ax3+bx2+11x−6f(x) = ax^3 + bx^2 + 11x - 6, defined on [1,3][1, 3], satisfies all the conditions of Rolle's theorem for c=2+13c = 2 + \dfrac{1}{\sqrt{3}}, then

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  4. Question 4

    12 May 2026 S2

    74
    If Rolle's theorem holds for the function f(x)=x3+px2+qx+5,x∈[1,3]f(x) = x^3 + px^2 + qx + 5, x \in [1, 3] with c=2+13c = 2 + \dfrac{1}{\sqrt{3}}, then the values of pp and qq are respectively...

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