SOLUTION —
Here, $m_1+m_2=\frac{-2 h}{b}$ and $m_1 m_2=\frac{a}{b}$
Given that, $\quad m_1=2 m_2$
$\begin{array}{ll}\therefore & 3 m_2=\frac{-2 h}{b} \\\text { and } & 2 m_2^2=\frac{a}{b} \Rightarrow 2\left(\frac{-2 h}{3 b}\right)^2=\frac{a}{b} \\\Rightarrow & 8 h^2=9 a b\end{array}$
So, The correct option will be (C).