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Questions › DSE › DSE 2021 › Q15
4 marks, −1Mathematics › Limits, continuity and differentiability › Mean value theorem and Rolle's theoremHardabout 3 min

DSE 2021 Question 15: Limits, continuity and differentiability

Let a1,a2,a3,…,ana_1, a_2, a_3, \dots, a_na1​,a2​,a3​,…,an​ be real numbers such that a1+a2+a3+⋯+an=0a_1 + a_2 + a_3 + \dots + a_n = 0a1​+a2​+a3​+⋯+an​=0. Suppose n≥5n \geq 5n≥5. Which of the following statements is true about the roots of q(x)=a1+2a2x+3a3x2+⋯+nanxn−1q(x) = a_1 + 2a_2 x + 3a_3 x^2 + \dots + n a_n x^{n-1}q(x)=a1​+2a2​x+3a3​x2+⋯+nan​xn−1?

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Let a₁, a₂, a₃, …, aₙ be real numbers such that a₁ + a₂ + a₃ + … + aₙ = 0. Suppose n ≥ 5. Which of the following statements is true about the roots of q(x) = a₁ + 2a₂ x + 3a₃ x² + … + n aₙ xⁿ⁻¹? (A) q(x) has at least one real root (B) q(x) has no real root (C) q(x) has (n-1) real roots (D) q(x) has (n-2) real roots

Also written as: Let a_1, a_2, a_3,..., a_n be real numbers such that a_1 + a_2 + a_3 +... + a_n = 0. Suppose n >= 5. Which of the following statements is true about the roots of q(x) = a_1 + 2a_2 x + 3a_3 x^2 +... + n a_n x^(n-1)?

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Mean value theorem and Rolle's theorem, part of Limits, continuity and differentiability in Mathematics.

Results linking the average rate of change to a derivative at some point.

TestStop has 13 past-paper questions on this subtopic.

Practise Limits, continuity and differentiabilityMore on Mean value theorem and Rolle's theorem

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