JEE Advanced 2020 Mathematics question
For a polynomial with real coefficients, let denote the number of distinct real roots of . Suppose is the set of polynomials with real coefficients defined by
S = {- + + + : , , , }.
For a polynomial , let and denote its first and second order derivatives, respectively. Then the minimum possible value of , where , is
Answer: 5
Solution
Every has and as repeated roots, so and . By Rolle's theorem applied to on , has at least one more root in ; hence (roots , some , and ). Applying Rolle's theorem to on and
See the full step-by-step solution
Create a free account to read the complete working, and practise questions like this in a timed test.
Create a free account