JEE Main 2022MathematicsApplication of DerivativesHardNumerical

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (27 Jun Shift 1)

Question

If the sum of all the roots of the equation e2x-11ex-45e-x+812=0 is logeP, then P is equal to _____.

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Show full solutionCorrect answer: 45
Correct answer
45

Step-by-step explanation

Given e2x-11ex-45ex+812=0

e3x-11e2x+812ex-45=0

Let ex=t, so t3-11t2+812t-45=0

Product of roots t1t2t3=45

i.e. ex1×ex2×ex3=45 

ex1+x2+x3=45

x1+x2+x3=log245  

Given sum of root =lnP

So P=45

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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.