If the arithmetic mean and geometric mean of the two roots of a quadratic equation are $9$ and $4$ respectively,then what is the quadratic equation?

If $\alpha, \beta$ are the roots of $ax^2 + bx + c = 0$ and $\alpha + \beta, \alpha^2 + \beta^2, \alpha^3 + \beta^3$ are in $G.P.$,where $\Delta = b^2 - 4ac$,then:

If $\alpha, \beta, \gamma$ are the roots of the equation $4x^3 + 12x^2 - 7x + 165 = 0$ and $\alpha + 5, \beta + 5, \gamma + 5$ are the roots of the equation $ax^3 + bx^2 + cx + d = 0$,then the product of the roots of the second equation is:

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

If one root of $x^3-7x^2+36=0$ is twice the other,then the sum of those two roots is

If the difference of the roots of $x^2 - px + 8 = 0$ is $2$,then the value of $p$ is