If $\alpha, \beta, \gamma, \delta$ are the roots of $x^4 - 100x^3 + 2x^2 + 4x + 10 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\delta}$ is equal to:

The harmonic mean of two numbers is $-\frac{8}{5}$ and their geometric mean is $2$. The quadratic equation whose roots are twice those numbers is

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of their squares,then:

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

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

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 2(m^2 + 1)x + m^4 + m^2 + 1 = 0$,then find the value of $\alpha^2 + \beta^2$.