If the roots of $ax^2 + bx + c = 0$ are $\alpha, \beta$ and the roots of $Ax^2 + Bx + C = 0$ are $\alpha - k, \beta - k$,then $\frac{B^2 - 4AC}{b^2 - 4ac}$ is equal to

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

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-9x^2+23x-15=0$,then $\alpha^3+\beta^3+\gamma^3=$

Two real numbers $\alpha$ and $\beta$ are such that $\alpha + \beta = 3$ and $|\alpha - \beta| = 4$. Then $\alpha$ and $\beta$ are the roots of the quadratic equation:

Let $\alpha, \beta, \gamma$ be the roots of the equation $x^3+px+q=0$ and $f(x)=3p^2x^2+p^2x+3q$. Then $\sum \alpha^2 \beta + \sum \alpha^4 =$

If one root of the equation $i x^2 - 2(i + 1) x + (2 - i) = 0$ is $(2 - i)$,then the other root is