jee-main 2023 Q61

jee-main · India · session2_12apr_shift1 Roots of polynomials Vieta's formulas: compute symmetric functions of roots

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 equal to
(1) 81
(2) 9
(3) 72
(4) 729

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 equal to\\
(1) 81\\
(2) 9\\
(3) 72\\
(4) 729

Paper Questions

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