JEE Main 2015MathematicsQuadratic EquationHardMCQ

JEE Main 2015 — Quadratic Equation Question with Solution

JEE Main 2015 (04 Apr)

Question

Let α and β be the roots of equation x2-6x-2=0. If an=αn-βn, ∀ n≥1, then the value of a10-2a82a9 is equal to

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Show full solutionCorrect option: D
Correct answer
D3

Step-by-step explanation

Given, α, β are roots of x2-6x-2=0.

⇒ α2-6α-2=0 and  β2-6β-2=0

⇒  α2-2=6α andβ2-2=6β  ...1

a10-2a82a9=α10-β10-2α8-β82α9-β9

=α10-2α8-β10-2β82α9-β9

= α 8 α 2 - 2 - β 8 β 2 - 2 2 α 9 - β 9

= α 8 6 α - β 8 6 β 2 α 9 - β 9        [ ∵  From (1)]

 =6α9-6β92α9-β9=3

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About this question

This is a previous-year question from JEE Main 2015, 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.