If $\alpha$ and $\beta$ are the roots of the equation $a x^2+b x+c=0$ and if $p x^2+q x+r=0$ has roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$,then $r$ is equal to

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,then what is the value of $\alpha \beta^2 + \alpha^2 \beta + \alpha \beta$?

If $a+b+c=1$,$ab+bc+ca=2$ and $abc=3$,then the value of $a^{4}+b^{4}+c^{4}$ is equal to $...$

The value of $a$ $(a \ge 3)$ for which the sum of the cubes of the roots of $x^2 - (a - 2)x + (a - 3) = 0$ assumes the least value is:

Let $\alpha$ and $\beta$ be the roots of $x^2-6x-2=0$,with $\alpha > \beta$. If $a_n = \alpha^n - \beta^n$ for $n \geq 1$,then the value of $\frac{a_{10}-2a_8}{2a_9}$ is

If $\alpha, \beta, \gamma$ and $\delta$ are zeroes of the polynomial equation $x^4-3x^2+6x-12=0$,then the value of $\frac{\alpha+\beta+\gamma}{\delta^2}+\frac{\alpha+\delta+\gamma}{\beta^2}+\frac{\alpha+\beta+\delta}{\gamma^2}+\frac{\delta+\beta+\gamma}{\alpha^2}$ is equal to