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

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Let $f(x)=5x^3-15x$; $f'(x)=0$ at $x=\pm1$ with $f(-1)=10$ (local max) and $f(1)=-10$ (local min). Three distinct real roots exist when $-10

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

Explanation

Reviewed by Dr. Abubacker

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