JEE Main 2020MathematicsApplication of DerivativesHardMCQ

JEE Main 2020 — Application of Derivatives Question with Solution

JEE Main 2020 (03 Sep Shift 2)

Question

Suppose fx is a polynomial of degree four having critical points at -1, 0, 1. If T=x∈R |fx=f0, then the sum of squares of all the elements of T is :

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Show full solutionCorrect option: A
Correct answer
A4

Step-by-step explanation

f'x=k.xx+1x-1

=kx3-x

Integrating both sides with respect to x, we get

fx=k x44-x22+c

⇒f0=c

∵  fx=f0

⇒kx4-2x24+c=c

⇒x2x2-2=0

⇒x=0, 2, -2

⇒T=0, 2, -2

Thus, sum of squares of all the elements of T is 02+22+-22=4.

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About this question

This is a previous-year question from JEE Main 2020, covering the Application of Derivatives 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.