Let $\alpha ,\beta ,\gamma$ be the roots of the equation $x^3+3a{x}^2+3bx+c=0$. If $\alpha ,\beta ,\gamma$ are in H.P. then $\beta$ is equal to -

If $\cos \alpha$ is a root of the equation $25x^2+5x-12=0,-1<x<0$, then the value of $\sin 2\alpha$ is

$\left(\mathrm{A}\right)$    $\frac{12}{25}$

$\left(\mathrm{B}\right) \frac{-12}{25}$

$\left(\mathrm{C}\right) \frac{-24}{25}$

$\left(\mathrm{D}\right) \frac{24}{25}$

Graph of $y=a{x}^2+bx+c$ is given adjacently. What conclusions can be drawn from this graph -