Let α,β be roots of x²-6x-2=0. If an=αⁿ-βⁿ for n 1, then a₁₀-2a₈ 2a₉ equals (a) 3 (b) -3 (c) 6 (d) -6

Correct answer: (a) 3 The roots satisfy an=6an-1+2an-2, so a₁₀-2a₈=6a₉, giving (6a₉)/(2a₉)=3. JEE Main 2014 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

JEE PYQ

[JEE Main 2014] Let $\alpha,\beta$ be roots of $x^2-6x-2=0$. If $a_n=\alpha^n-\beta^n$ for $n\ge1$, then $\dfrac{a_{10}-2a_8}{2a_9}$ equals

VAVidaara Admin Asked 1mo ago 2 views 1 answer

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Let $\alpha,\beta$ be roots of $x^2-6x-2=0$. If $a_n=\alpha^n-\beta^n$ for $n\ge1$, then $\dfrac{a_{10}-2a_8}{2a_9}$ equals

(a) $3$
(b) $-3$
(c) $6$
(d) $-6$

1 Answer

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

Correct answer: (a) $3$

The roots satisfy $a_n=6a_{n-1}+2a_{n-2}$, so $a_{10}-2a_8=6a_9$, giving $\frac{6a_9}{2a_9}=3$.

JEE Main 2014 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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