For the quadratic equation $4x^2 + 3x + 7 = 0$,if $\alpha$ and $\beta$ are the roots,then find the value of $1/\alpha + 1/\beta$.

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If the roots of the equation $x^2 - 5x + 16 = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + px + q = 0$ are $\alpha^2 + \beta^2$ and $\frac{\alpha \beta}{2}$,then:

The roots of the quadratic equation $3x^2 - px + q = 0$ are the $10^{\text{th}}$ and $11^{\text{th}}$ terms of an arithmetic progression with a common difference $d = \frac{3}{2}$. If the sum of the first $11$ terms of this arithmetic progression is $88$,then $q - 2p$ 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

If $\alpha, \beta, \gamma$ are the roots of the equation $2x^3 - 3x^2 + 5x - 7 = 0$,then $\sum \alpha^2 \beta^2 =$