What is the geometric mean of the roots of the equation $x^2 - 18x + 9 = 0$?

For the equation $2x^2 + 2(a + b)x + a^2 + b^2 = 0$,if $\alpha$ and $\beta$ are the roots,then the equation whose roots are $(\alpha + \beta)^2$ and $(\alpha - \beta)^2$ is:

If the sum of the roots of a quadratic equation is $1$ and the sum of the squares of the roots is $13$,then find the equation.

If $\alpha, \beta$ are the roots of $x^2+ax+2=0$ and $\frac{1}{\alpha}, \frac{1}{\beta}$ are the roots of $x^2-bx+c=0$,then $\left(\alpha+\frac{1}{\beta}\right)\left(\beta+\frac{1}{\alpha}\right)\left(\alpha-\frac{1}{\alpha}\right)\left(\beta-\frac{1}{\beta}\right) = $

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

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