jee-main 2023 Q61

jee-main · India · session2_13apr_shift2 Roots of polynomials Vieta's formulas: compute symmetric functions of roots

Let $\alpha , \beta$ be the roots of the equation $x ^ { 2 } - \sqrt { 2 } x + 2 = 0$. Then $\alpha ^ { 14 } + \beta ^ { 14 }$ is equal to
(1) $- 64$
(2) $- 64 \sqrt { 2 }$
(3) $- 128$
(4) $- 128 \sqrt { 2 }$

Let $\alpha , \beta$ be the roots of the equation $x ^ { 2 } - \sqrt { 2 } x + 2 = 0$. Then $\alpha ^ { 14 } + \beta ^ { 14 }$ is equal to\\
(1) $- 64$\\
(2) $- 64 \sqrt { 2 }$\\
(3) $- 128$\\
(4) $- 128 \sqrt { 2 }$

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