If $\alpha$ and $\beta$ are the roots of the quadratic equation $ax^{2}+bx+c=0$ and $3b^{2}=16ac$, then:

If the roots of the equation $ax^2 + bx + c = 0$ are $\sin \alpha$ and $\cos \alpha$,then:

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 + qx - r = 0$,then find the equation whose roots are $\left( \beta \gamma + \frac{1}{\alpha} \right), \left( \gamma \alpha + \frac{1}{\beta} \right), \left( \alpha \beta + \frac{1}{\gamma} \right)$.

If the coefficients of the equation whose roots are $k$ times the roots of the equation $x^3+\frac{1}{4} x^2-\frac{1}{16} x+\frac{1}{144}=0$ are integers,then a possible value of $k$ is

If the roots of the equation $x^2 + px + q = 0$ are $p$ and $q$,then what must be the value of $p$?

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is