JEE Main 2021MathematicsQuadratic EquationMediumNumerical

JEE Main 2021 — Quadratic Equation Question with Solution

JEE Main 2021 (26 Feb Shift 2)

Question

Let α and β be two real numbers such that α+β=1 and αβ=-1. Let pn=αn+βn, pn-1=11 and pn+1=29 for some integer n⩾1. Then, the value of pn2 is______.

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Show full solutionCorrect answer: 324
Correct answer
324

Step-by-step explanation

x2-x-1=0 roots =α,β

α2-α-1=0⇒αn+1=αn+αn-1β2-β-1=0⇒βn+1=βn+βn-1                           +                           pn+1=pn+pn-1

29=pn+11

pn=18

pn2=324

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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.