jee-main 2023 Q61

jee-main · India · session2_08apr_shift1 Roots of polynomials Vieta's formulas: compute symmetric functions of roots

Let $\alpha , \beta , \gamma$ be the three roots of the equation $x ^ { 3 } + b x + c = 0$ if $\beta \gamma = 1 = - \alpha$ then $b ^ { 3 } + 2 c ^ { 3 } - 3 \alpha ^ { 3 } - 6 \beta ^ { 3 } - 8 \gamma ^ { 3 }$ is equal to
(1) $\frac { 155 } { 8 }$
(2) 21
(3) $\frac { 169 } { 8 }$
(4) 19

Let $\alpha , \beta , \gamma$ be the three roots of the equation $x ^ { 3 } + b x + c = 0$ if $\beta \gamma = 1 = - \alpha$ then $b ^ { 3 } + 2 c ^ { 3 } - 3 \alpha ^ { 3 } - 6 \beta ^ { 3 } - 8 \gamma ^ { 3 }$ is equal to\\
(1) $\frac { 155 } { 8 }$\\
(2) 21\\
(3) $\frac { 169 } { 8 }$\\
(4) 19

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