JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Hard

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Analyzing +4 | -1

If the equation

a_n x^n+a_{n-1} x^{n-1}+\ldots+a_1 x=0, a_1 \neq 0

n \geq 2

, has a positive root

x=\alpha

, then the equation

n a_n x^{n-1}+(n-1) a_{n-1} x^{n-2}+\ldots+a_1=0

has a positive root, which is

View answer and explanation

Correct option: D

smaller than

\alpha

Option D (smaller than

\alpha

) is correct because by Rolle's theorem, there exists a root of the derivative between 0 and

\alpha

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