JEE Main 2021MathematicsQuadratic EquationMediumNumerical

JEE Main 2021 — Quadratic Equation Question with Solution

JEE Main 2021 (27 Jul Shift 2)

Question

The number of real roots of the equation e4x-e3x-4e2x-ex+1=0 is equal to

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

We have, e4x-e3x-4e2x-ex+1=0

Let ex=t, we get

t4-t3-4t2-t+1=0

Divide with t2 on both sides

⇒t2-t-4-1t+1t2=0

⇒t+1t2-t+1t-6=0

Let α=t+1t≥2, we get

α2-α-6=0

⇒α-3α+2=0

⇒α=3,-2 (reject)

⇒t+1t=3⇒t2-3t+1=0

⇒ex=3±52

⇒ex=3±2.232∵5≈2.23

⇒ex=5.232 or ex=0.772

⇒ex=2.615 or ex=0.385

⇒ The number of real roots =2.

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About this question

This is a previous-year question from JEE Main 2021, 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.