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AlgebraGeneralInteger TypeVery Hard
Q17.Let S={(x2−1)2(a0+a1x+a2x2+a3x3):a0,a1,a2,a3∈R}S=\{(x^2-1)^2(a_0+a_1x+a_2x^2+a_3x^3):a_0,a_1,a_2,a_3\in\mathbb{R}\}. For a polynomial gg, let mgm_g denote the number of distinct real roots of gg. For f∈Sf\in S, find the minimum possible value of (mf′+mf′′)(m_{f'}+m_{f''}).
Subjective / proof problem — work it out in the Scratchpad, then reveal the solution.
citeJEE (Advanced) 2020 — Mathematics — Paper 1
2020id · 902f9019
Subjective — no options to pick