If $2, 3, 6$ are the roots of the polynomial $f(x) = x^3 + ax^2 + bx + c$,where $a, b, c \in \mathbb{C}$. Then,the value of $a - c$ is

The $H.M.$ between the roots of the equation $x^2 - 10x + 11 = 0$ is

Let $\alpha$ and $\beta$ be the roots of the equation $p x^2 + q x + r = 0$,where $p \neq 0$. If $p, q, r$ are in $AP$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is

Given that $\tan \alpha$ and $\tan \beta$ are the roots of $x^2 - px + q = 0$,then the value of $\sin^2(\alpha + \beta)$ is:

If the ratio of the roots of the equations $x^2 + bx + c = 0$ and $x^2 + qx + r = 0$ is the same,then:

The sum of the cubes of all the roots of the equation $x^{4}-3x^{3}-2x^{2}+3x+1=10$ is