If the extreme value of $3 x-2 x^2+1$ is $k$, then the set of all real values of $x$ for which $k x^2+2 x+1>0$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-5 x^2-2 x+24=0$, then $\frac{\beta \gamma}{\alpha}+\frac{\gamma \alpha}{\beta}+\frac{\alpha \beta}{\gamma}=$

Let $p(x)$ be a quadratic polynomial with real coefficients. If $p(x)=0$ has only purely imaginary roots, then the zeroes of the polynomial $p(p(x))$ are

If $\alpha, \beta, \gamma$ are the roots of the equation $4 x^3+12 x^2-7 x+165=0$ and $\alpha+5, \beta+5, \gamma+5$ are the roots of the equation $a x^3+b x^2+c x+d=0$ then the product of the roots of the second equation is