If α,β are the roots of x²-x+1=0, then α²⁰⁰⁹+β²⁰⁰⁹= (a) -1 (b) 1 (c) 2 (d) -2

Correct answer: (b) 1 α,β=e^± iπ/3; α²⁰⁰⁹+β²⁰⁰⁹=2cos 2009π 3=2cos 5π 3=1. JEE Main 2010 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

JEE PYQ

[JEE Main 2010] If $\alpha,\beta$ are the roots of $x^2-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$

VAVidaara Admin Asked 1mo ago 2 views 1 answer

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If $\alpha,\beta$ are the roots of $x^2-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$

(a) $-1$
(b) $1$
(c) $2$
(d) $-2$

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 1mo ago ▲ 0

Correct answer: (b) $1$

$\alpha,\beta=e^{\pm i\pi/3}$; $\alpha^{2009}+\beta^{2009}=2\cos\frac{2009\pi}3=2\cos\frac{5\pi}3=1$.

JEE Main 2010 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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