JEE Main 2023MathematicsQuadratic EquationMediumMCQ

JEE Main 2023 — Quadratic Equation Question with Solution

JEE Main 2023 (13 Apr Shift 2)

Question

Let α, β  be the roots of the equation x2-2x+2=0 Then α14+β14 is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C-128

Step-by-step explanation

Given,

x2-2x+2=0

⇒x=2±6i2

⇒x=21±3i2

⇒x=212±3i2

⇒x=2cosπ3±isinπ3

So, α=2cosπ3+isinπ3=2eiπ3

And β=2cosπ3-isinπ3=2e-iπ3

Now α14+β14=2eiπ314+2e-iπ314

⇒α14+β14=214ei14π3+e-i14π3

⇒α14+β14=214cos14π3+isin14π3+cos14π3-isin14π3

⇒α14+β14=272cos14π3

⇒α14+β14=28cos4π+2π3

⇒α14+β14=28cos2π3

⇒α14+β14=-28×12=-128

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About this question

This is a previous-year question from JEE Main 2023, 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.