JEE Main 2012 — Quadratic Equation Question with Solution
JEE Main 2012 (19 May Online)
Question
Consider a quadratic equation , where and let .
Statement 1: The quadratic equation has at least one root in the interval .
Statement 2: The Rolle's theorem is applicable to function on the interval .
Choose an option
Show full solutionCorrect option: D
Correct answer
DStatement 1 is true, Statement 2 is true, , Statement 2 is a correct explanation for Statement 1.
Step-by-step explanation
Let
Given: and
Statement-2:
(i) and
(ii) is continuous on and differentiable on
By Rolle's theorem such that
This holds the statement 2. Also, from statement-2, we can say has at least one root in .
Thus statement-1 and 2 both are true and statement-2 is a correct explanation for statement-1.
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This is a previous-year question from JEE Main 2012, covering the Quadratic Equation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.