If the set of all values of a, for which the equation $5 x^3-15 x-a=0$ has three distinct real roots, is the interval $(\alpha, \beta)$, then $\beta-2 \alpha$ is equal to ______

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Aicharya · Accepted Answer

$\begin{aligned} & 5 x^3-15 x-a=0 \ & f(x)=5 x^3-15 x \ & f(x)=15 x^2-15=15(x-1)(x+1)\end{aligned}$ $\mathrm{a} \in(-10,10)$ $\alpha=-10, \beta=10$ $\beta-2 \alpha=10+20=30$

If the set of all values of a, for which the equation $5 x^3-15 x-a=0$ has three distinct real roots, is the…

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