Let be the roots of the quadratic equation

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

\alpha, \beta

be the roots of the quadratic equation

x^2 + \sqrt{6}x + 3 = 0

. Then

\frac{\alpha^{23} + \beta^{23} + \alpha^{14} + \beta^{14}}{\alpha^{15} + \beta^{15} + \alpha^{10} + \beta^{10}}

is (A) 729 (B) 72 (C) 81 (D) 9