If $\alpha$ and $\beta$ are the roots of the equation $x^2 + ax + b = 0$,then the value of $\alpha^3 + \beta^3$ is equal to:

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

If the arithmetic mean and harmonic mean of the roots of a quadratic equation are $3/2$ and $4/3$ respectively,then what is the equation?

The value of $k$ for which one of the roots of ${x^2} - x + 3k = 0$ is double of one of the roots of ${x^2} - x + k = 0$ is

If $\alpha, \beta, \gamma$ and $\delta$ are zeroes of the polynomial equation $x^4-3x^2+6x-12=0$,then the value of $\frac{\alpha+\beta+\gamma}{\delta^2}+\frac{\alpha+\delta+\gamma}{\beta^2}+\frac{\alpha+\beta+\delta}{\gamma^2}+\frac{\delta+\beta+\gamma}{\alpha^2}$ is equal to

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