The sum of the roots of a quadratic equation is $2$ and the sum of their cubes is $98$. Then the equation is:

For the equation $3x^2 + px + 3 = 0, p > 0$,if one of the roots is the square of the other,then $p$ is equal to:

Let $\alpha, \beta$ be roots of $x^2+\sqrt{2}x-8=0$. If $U_n = \alpha^n + \beta^n$,then $\frac{U_{10} + \sqrt{2}U_9}{2U_8}$ is equal to ............

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 $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$,then the coefficient of $x$ in the cubic equation whose roots are $\alpha(\beta+\gamma), \beta(\gamma+\alpha)$ and $\gamma(\alpha+\beta)$ is

If the roots of the equation $x^2 + bx + ac = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + ax + bc = 0$ are $\alpha, \gamma$,then what are the values of $\alpha, \beta, \gamma$ respectively?