JEE MAIN - Mathematics (2025 - 23rd January Morning Shift - No. 22)
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 _________.
Answer
30
Explanation
$$\begin{aligned} & 5 x^3-15 x-a=0 \\ & f(x)=5 x^3-15 x \\ & f'(x)=15 x^2-15=15(x-1)(x+1) \end{aligned}$$
_23rd_January_Morning_Shift_en_22_1.png)
$$\begin{aligned} &\mathrm{a} \in(-10,10)\\ &\alpha=-10, \beta=10\\ &\beta-2 \alpha=10+20=30 \end{aligned}$$
Comments (0)
