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

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 35x + 2 = 0$,then the value of $(2\alpha - 35)^3 \cdot (2\beta - 35)^3$ is equal to

If $(\alpha+\sqrt{\beta})$ and $(\alpha-\sqrt{\beta})$ are the roots of the equation $x^{2}+px+q=0$, where $\alpha, \beta, p$ and $q$ are real, then the roots of the equation $(p^{2}-4q)(p^{2}x^{2}+4px)-16q=0$ are

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are:

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 + qx - r = 0$,then find the equation whose roots are $\left( \beta \gamma + \frac{1}{\alpha} \right), \left( \gamma \alpha + \frac{1}{\beta} \right), \left( \alpha \beta + \frac{1}{\gamma} \right)$.

If $\alpha, \beta$ are the roots of $x^2 - ax + b = 0$ and if $\alpha^n + \beta^n = V_n$,then -