Applications of Derivatives
Application of Derivatives
nta_pyq_2025_jan
Grade 12
Question:
If the set of all values of a, for which the equation 5x - 15x - a = 0 has three distinct real roots, is the interval 3 (\alpha, \beta) , then \beta - 2\alpha is equal to ______
Step-by-Step Solution
Key Concept: Apply the core result for monotonicity, tangents and extrema and simplify using the given constraints.
5x - 15x - a = 0 3 3 (30) f (x) = 5x - 15x 2 f (x) = 15x - 15 = 15(x - 1)(x + 1) a \in (-10, 10) \alpha = -10, \beta = 10 \beta - 2\alpha = 10 + 20 = 30
Correct Answer: 30