JEE MATHEMATICS MCQ: THEORY OF EQUATION

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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

has a positive root

\alpha

, then the equation

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

has

View answer and explanation

Correct option: A

A positive root less than

\alpha

Option A is correct because by applying Rolle's theorem to a related function, we can show that the given equation has a positive root less than α.

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