JEE Math Practice Question
Let $a, b, c$ be three non-zero real numbers such that the equation \[ \sqrt{3} a \cos x+2 b \sin x=c, x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \] has two distinct real roots $\alpha$ and $\beta$ with $\alpha+\beta=\frac{\pi}{3}$. Then, what is the value of $\frac{b}{a}$?
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