Verified Solution • 2025–26 Session moderate

QJEEM25Ma8e9c: JEE Main 2025 Mathematics - Class 12 JEEM25Ma8e9c Solution: If the set of all values of , for which the equation has three…

If the set of all values of aa , for which the equation 5x3−15x−a=05 x^3-15 x-a=0 has three distinct real roots, is the interval (α,β)(\alpha, \beta) , then β−2α\beta-2 \alpha is equal to _________.

Step-by-Step Verified Solution

amp;5x3−15x−a=0amp;f(x)=5x3−15xamp;f′(x)=15x2−15=15(x−1)(x+1)\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}

JEE Main 2025 (Online) 23rd January Morning Shift Mathematics - Application of Derivatives Question 5 English Explanation

amp;a∈(−10,10)amp;α=−10,β=10amp;β−2α=10+20=30\begin{aligned}&\mathrm{a} \in(-10,10)\\&\alpha=-10, \beta=10\\&\beta-2 \alpha=10+20=30\end{aligned}

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