jee-main 2013 Q61

jee-main · India · 25apr Roots of polynomials Vieta's formulas: compute symmetric functions of roots

If $p$ and $q$ are non-zero real numbers and $\alpha ^ { 3 } + \beta ^ { 3 } = - p , \alpha \beta = q$, then a quadratic equation whose roots are $\frac { \alpha ^ { 2 } } { \beta } , \frac { \beta ^ { 2 } } { \alpha }$ is :
(1) $p x ^ { 2 } - q x + p ^ { 2 } = 0$
(2) $q x ^ { 2 } + p x + q ^ { 2 } = 0$
(3) $p x ^ { 2 } + q x + p ^ { 2 } = 0$
(4) $q x ^ { 2 } - p x + q ^ { 2 } = 0$

If $p$ and $q$ are non-zero real numbers and $\alpha ^ { 3 } + \beta ^ { 3 } = - p , \alpha \beta = q$, then a quadratic equation whose roots are $\frac { \alpha ^ { 2 } } { \beta } , \frac { \beta ^ { 2 } } { \alpha }$ is :\\
(1) $p x ^ { 2 } - q x + p ^ { 2 } = 0$\\
(2) $q x ^ { 2 } + p x + q ^ { 2 } = 0$\\
(3) $p x ^ { 2 } + q x + p ^ { 2 } = 0$\\
(4) $q x ^ { 2 } - p x + q ^ { 2 } = 0$

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