Let two numbers have an arithmetic mean of $9$ and a geometric mean of $4$. Then these numbers are the roots of the quadratic equation:

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 - x - 1 = 0$,then what is the value of $\left( \frac{1 + \alpha}{1 - \alpha} \right) \left( \frac{1 + \beta}{1 - \beta} \right) \left( \frac{1 + \gamma}{1 - \gamma} \right)$?

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

If $p$ and $q$ are the roots of the equation $x^{2}+px+q=0$, then:

If $\alpha$ and $\beta$ are the roots of the equation $2x(2x+1)=1$,then $\beta$ is equal to

The expression $x^3 - 3x^2 - 9x + c$ can be written in the form $(x - a)^2 (x - b)$ if the value of $c$ is