The $G.M.$ of the roots of the equation $x^2 - 18x + 9 = 0$ is

If $\alpha$ and $\beta$ are the roots of $x^2+7x+3=0$ and $\frac{2\alpha}{3-4\alpha}, \frac{2\beta}{3-4\beta}$ are the roots of $ax^2+bx+c=0$ and $GCD(a, b, c) = 1$,then $a+b+c=$

If one root of $ax^2 + bx + c = 0$ is the square of the other,then the value of $b^3 + ac^2 + a^2c$ is

The condition that one root of the equation $ax^2 + bx + c = 0$ is three times the other is:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 2x + 3 = 0$,then the equation whose roots are $\frac{1}{\alpha^2}$ and $\frac{1}{\beta^2}$ is

If $p$ and $q$ are non-zero real numbers and $\alpha^3 + \beta^3 = -p$,$\alpha \beta = q$,then a quadratic equation whose roots are $\frac{\alpha^2}{\beta}$ and $\frac{\beta^2}{\alpha}$ is