jee-main 2025 Q61

jee-main · India · session2_08apr_shift1 Roots of polynomials Vieta's formulas: compute symmetric functions of roots
Q61. Let $\alpha , \beta$ be the roots of the equation $x ^ { 2 } + 2 \sqrt { 2 } x - 1 = 0$. The quadratic equation, whose roots are $\alpha ^ { 4 } + \beta ^ { 4 }$ and $\frac { 1 } { 10 } \left( \alpha ^ { 6 } + \beta ^ { 6 } \right)$, is :
(1) $x ^ { 2 } - 190 x + 9466 = 0$
(2) $x ^ { 2 } - 180 x + 9506 = 0$
(3) $x ^ { 2 } - 195 x + 9506 = 0$
(4) $x ^ { 2 } - 195 x + 9466 = 0$
Q61. Let $\alpha , \beta$ be the roots of the equation $x ^ { 2 } + 2 \sqrt { 2 } x - 1 = 0$. The quadratic equation, whose roots are $\alpha ^ { 4 } + \beta ^ { 4 }$ and $\frac { 1 } { 10 } \left( \alpha ^ { 6 } + \beta ^ { 6 } \right)$, is :\\
(1) $x ^ { 2 } - 190 x + 9466 = 0$\\
(2) $x ^ { 2 } - 180 x + 9506 = 0$\\
(3) $x ^ { 2 } - 195 x + 9506 = 0$\\
(4) $x ^ { 2 } - 195 x + 9466 = 0$