If the roots of the equation $x^2 + px + q = 0$ are $p$ and $q$,then what must be the value of $p$?

If the harmonic mean of the roots of the equation $\sqrt{2} x^2 - bx + (8 - 2\sqrt{5}) = 0$ is $4$,then the value of $b$ is

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

If $\alpha, \beta$ are the roots of the equation $x^2+bx+c=0$ satisfying the conditions $\alpha+\beta=5$ and $\alpha^3+\beta^3=60$,then $3c+2=$ (in $b$)

If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$,then the quadratic equation whose roots are $\sqrt{5} \alpha, \sqrt{5} \beta$ is

If the product of the roots of the equation $x^2+4kx+12e^{3\log k}-1=0$ where $k>0$ is $323$,then the sum of its roots is: