If one root of the equation $x^2 + px + q = 0$ is $2 + \sqrt{3}$,then the values of $p$ and $q$ are:

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4-8x^3+11x^2+32x-60=0$ and $\alpha < \beta < \gamma < \delta$,then $4\alpha+3\beta+2\gamma+\delta=$

The sum of all the roots of the equation $(x-1)^{2}-5|x-1|+6=0$ is:

If the roots of the equation $(m - n)x^2 + (n - l)x + (l - m) = 0$ are equal,then which of the following is true for $l, m,$ and $n$?

If the quadratic equation $(\lambda + 2)x^2 - 3\lambda x + 4\lambda = 0, \lambda \neq -2$,has two positive roots,then the number of possible integral values of $\lambda$ is:

If $\alpha$ and $\beta$ are the roots of $x^2+3(a+3)x-9a=0$ such that the roots are equal for different values of $a$ (where $\alpha > \beta$ is not applicable as roots are equal,but let $\alpha$ be the root for $a=-9$ and $\beta$ be the root for $a=-1$),then the minimum value of the expression $x^2+\alpha x-\beta$ is: