If the sum of all the roots of the equation $e^{2x}-11e^x-45e^{-x}+\frac{81}{2}=0$ is $\log_e p$, then p is equal to ____________.

JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 June 2022, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

If the sum of all the roots of the equation

e^{2x}-11e^x-45e^{-x}+\frac{81}{2}=0

\log_e p

, then p is equal to ____________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Exponential Reducible to Quadratic

Same idea in other shifts

Asked 11× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.