JEE Main 2021 — Definite Integration Question with Solution
From: JEE Main 2021 (Online) 27th July Evening Shift
Question
Let f : (a, b) R be twice differentiable function such that for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least :
Choose an option
Show full solutionCorrect option: C
Correct answer
Cseven roots in (a, b)
Step-by-step explanation
f′(x) = g(x)
f′'(x) = g'(x)
Given, g(x).g'(x) = 0
f′(x).f′'(x) = 0
Also given f(x) has exactly 5 roots.
So from Rolle's theorem we can say,
f′(x) has 4 roots and f′'(x) has 3 roots.
f′(x).f′'(x) = 0 has 4 + 3 = 7 roots.
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