JEE Main 2022MathematicsApplication of DerivativesHardMCQ

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (24 Jun Shift 2)

Question

The number of distinct real roots of the equation x7-7x-2=0 is

Choose an option

Show full solutionCorrect option: D
Correct answer
D3

Step-by-step explanation

Given,

x7-7x-2=0

x7-7x=2

Now taking fx=x7-7x (odd) & y=2

Now differentiating fx w.r.t x we get,

f'x=7x6-1=7x2-1x4+x2+1

f'x=0⇒x=±1

So points of extrema are -1 & 1 , Now plotting the graph to check number of solution we get,

fx=2 has 3 real distinct solution.

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About this question

This is a previous-year question from JEE Main 2022, 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.