The $H.M.$ between the roots of the equation $x^2 - 10x + 11 = 0$ is

If one root of the equation $ax^3+bx+c=0$ is twice another root,then

Suppose $\alpha, \beta, \gamma$ are the roots of $x^3+x^2+x+2=0$. Then,the value of $\left(\frac{\alpha+\beta-2 \gamma}{\gamma}\right)\left(\frac{\beta+\gamma-2 \alpha}{\alpha}\right)\left(\frac{\gamma+\alpha-2 \beta}{\beta}\right)$ is

If $\sin 2 \theta$ and $\cos 2 \theta$ are solutions of $x^2+bx-c=0$,then

If $2$ and $3$ are two roots of the equation $2x^3 + mx^2 - 13x + n = 0$,then the values of $m$ and $n$ are respectively

If the sum of the roots of the equation $\lambda x^2 + 2x + 3\lambda = 0$ is equal to their product,then $\lambda = $