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

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 5x + 16 = 0$,and if $\alpha^2 + \beta^2$ and $\alpha\beta/2$ are the roots of the equation $x^2 + px + q = 0$,then:

If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then

Let $f(x)$ be a quadratic polynomial such that $f(-2) + f(3) = 0$. If one of the roots of $f(x) = 0$ is $-1$,then the sum of the roots of $f(x) = 0$ is equal to

Assume that $\alpha, \beta, \gamma$ are the roots of $2x^3+5x^2+5x+2=0$. For $h \in R$,if $\alpha+h, \beta+h, \gamma+h$ are roots of $a(h)x^3+b(h)x^2+c(h)x+d(h)=0$,then:

Let $\alpha$ and $\beta$ be the roots of the equation $px^2+qx-r=0$,where $p \neq 0$. If $p, q,$ and $r$ are the consecutive terms of a non-constant $G$.$P$. and $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}$,then the value of $(\alpha-\beta)^2$ is: