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JEE Main 202523 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Application of Derivatives

JEE Main 2025 · 23 January · Morning Shift · Mathematics · Application of Derivatives

If the set of all values of a, for which the equation 5 x^3-15...

If the set of all values of a, 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 ______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 (α,

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5x3−15x−a=0f(x)=5x3−15xf(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} 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 (α,
a∈(−10,10)α=−10,β=10β−2α=10+20=30\mathrm{a} \in(-10,10) \alpha=-10, \beta=10 \beta-2 \alpha=10+20=30
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