JEE Main 2022MathematicsQuadratic EquationMediumMCQ

JEE Main 2022 — Quadratic Equation Question with Solution

JEE Main 2022 (24 Jun Shift 1)

Question

If the sum of the squares of the reciprocals of the roots α and β of the equation 3x2+λx-1=0 is 15, then 6α3+β32 is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C24

Step-by-step explanation

Given 1α2+1β2=15

For equation 3x2+λx-1=0

 α+β=-λ3, αβ=-13⇒α2β2=19

then α2+β2=α+β2-2αβ=λ29-2-13=λ29+23

 ⇒α2+β2=λ2+69

Now 1α2+1β2=15⇒α2+β2α2β2=15

⇒λ2+69×1α2β2=15  ⇒λ2+69×119=15

⇒λ2+6=15 ⇒λ=±3

Now 6α3+β32 =6α+βα2-αβ+β22

=6×1×159+132

=6×1×22=6×4=24

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Quadratic Equation chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.