Which equation has roots that are the squares of the roots of the equation $ax^2 + bx + c = 0$?

If $\alpha, \beta$ are the roots of $x^2-5 \gamma x-6 \delta=0$ and $\gamma, \delta$ are the roots of $x^2-5 \alpha x-6 \beta=0$,then $\alpha+\beta+\gamma+\delta=$

Let $p$ and $q$ be real numbers such that $p \neq 0$,$p^3 \neq q$,and $p^3 \neq -q$. If $\alpha$ and $\beta$ are nonzero complex numbers satisfying $\alpha+\beta = -p$ and $\alpha^3+\beta^3 = q$,then a quadratic equation having $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ as its roots is

The coefficient of $x$ in the equation $x^2 + px + q = 0$ was taken as $17$ in place of $13$. Its roots were found to be $-2$ and $-15$. The roots of the original equation are:

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + x + 5 = 0$,then $y = \sum \alpha^2 + \alpha \beta \gamma$ satisfies which of the following equations?

For what value of $m$ will one root of $x^2 - 3x + 2m = 0$ be double one root of $x^2 - x + m = 0$?