JEE Main 2022MathematicsQuadratic EquationMediumNumerical

JEE Main 2022 — Quadratic Equation Question with Solution

JEE Main 2022 (26 Jun Shift 1)

Question

The sum of the cubes of all the roots of the equation x4-3x3-2x2+3x+1=0 is _____.

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Show full solutionCorrect answer: 36
Correct answer
36

Step-by-step explanation

x4-3x3-2x2+3x+1=0

Dividing by x2 as x≠0

x2-3x-2+3x+1x2=0

x2+1x2-2+2-3x-1x-2=0

x-1x2-3x-1x=0

x-1x=0,x-1x=3

x2-1=0,x2-3x-1=0

x=±1

For x2-3x-1=0 let the roots are γ & δ

α=1,β=-1, γ+δ=3,γδ=-1

α3+β3+γ3+δ3

=1-1+γ+δγ+δ2-3γδ

=39-3-1=36

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About this question

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