If the roots of $x^4-10x^3+37x^2-60x+36=0$ are $\alpha, \alpha, \beta, \beta$ with $\alpha < \beta$,then find the value of $2\alpha+3\beta-2\alpha\beta$.

If the roots of the equation $qx^2 + px + q = 0$,where $p$ and $q$ are real,are complex,then the roots of the equation $x^2 - 4qx + p^2 = 0$ are

Statement-$I$: If $a + b + c = 0$ and $a, b, c$ are rational,then the roots of the equation $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ are rational.
Statement-$II$: The discriminant of $(b + c - a)x^2 + (c + a - b)x + (a + b - c) = 0$ is a perfect square.

Let $f(x) = x^2 + ax + b$,where $a, b \in R$. If $f(x) = 0$ has all its roots imaginary,then the roots of $f(x) + f'(x) + f''(x) = 0$ are

If the equation $(m - n)x^2 + (n - l)x + l - m = 0$ has equal roots,then $l, m,$ and $n$ satisfy:

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+2x^2-x-2=0$,then $\alpha^6+\beta^6+\gamma^6=$