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Best answer

In general, for a quadratic equation $ax^{2}+bx+c=0$ , sum of roots is given by : $\frac{-b}{a}$ and product of roots by : $\frac{-c}{a}$

$\therefore$ Here both the roots are $\beta$.

So, according to the given quadratic equation, we have

- $2\beta=\frac{b}{a}\quad \to (1)$ and
- $\beta^{2}=\frac{c}{a}\quad \to (2)$

Multiplying equations $(1)$ and $(2)$ and simplifying, we get $\beta^{3}=\frac{bc}{2a^{2}}$

Option C is correct