JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
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 ______
- A 10
- B 20
- C 30
- D 40
Answer & Solution
Correct Answer
(C) 30
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 5 x^3-15 x-a=0 \\ & f(x)=5 x^3-15 x \\ & f(x)=15 x^2-15=15(x-1)(x+1)\end{aligned}\) \(\mathrm{a} \in(-10,10)\) \(\alpha=-10, \beta=10\) \(\beta-2 \alpha=10+20=30\)
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