jee-main 2021 Q61

jee-main · India · session3_20jul_shift1 Complex Numbers Arithmetic Powers of i or Complex Number Integer Powers

If $\alpha$ and $\beta$ are the distinct roots of the equation $x ^ { 2 } + ( 3 ) ^ { \frac { 1 } { 4 } } x + 3 ^ { \frac { 1 } { 2 } } = 0$, then the value of $\alpha ^ { 96 } \left( \alpha ^ { 12 } - 1 \right) + \beta ^ { 96 } \left( \beta ^ { 12 } - 1 \right)$ is equal to:
(1) $56 \times 3 ^ { 25 }$
(2) $56 \times 3 ^ { 24 }$
(3) $52 \times 3 ^ { 24 }$
(4) $28 \times 3 ^ { 25 }$

If $\alpha$ and $\beta$ are the distinct roots of the equation $x ^ { 2 } + ( 3 ) ^ { \frac { 1 } { 4 } } x + 3 ^ { \frac { 1 } { 2 } } = 0$, then the value of $\alpha ^ { 96 } \left( \alpha ^ { 12 } - 1 \right) + \beta ^ { 96 } \left( \beta ^ { 12 } - 1 \right)$ is equal to:\\
(1) $56 \times 3 ^ { 25 }$\\
(2) $56 \times 3 ^ { 24 }$\\
(3) $52 \times 3 ^ { 24 }$\\
(4) $28 \times 3 ^ { 25 }$

Paper Questions

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