JEE Main · Maths · Application of Derivatives
Polynomial Root Counting
JEE Main asked Polynomial Root Counting 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2022. It belongs to Rolle's Theorem, in Application of Derivatives (Maths). The longest wait between two years asking it was 1 year.
Updated 2026-10-24
- Times asked
- 2
- in 2 shifts
- Years
- 2 of 8
- First asked
- 2021
- last in 2022
- Pattern
- Occasional
- across the analysed shifts
Questions on this idea a shift, by year
2017–2026. Asked in 2021 and 2022. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.
Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.
Shift by shift
Each square is one analysed shift, in date order. Open a filled one for that paper.
How JEE Main framed it
Numerical value is the usual form. Skill tested: application.
- Count real roots of polynomial equation
- Interval containing real root of polynomial
Difficulty
1 of the 2 questions had a numerical answer.
Every question
All 2 questions
From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.
- 24 Jun 2022, Shift 2 · Q11The number of distinct real roots of the equation isMediumSingle correct
- 26 Feb 2021, Shift 2 · Q84Let a be an integer such that all the real roots of the polynomial lie in the interval . Then,…MediumNumerical value
Shifts: 26 Feb 2021, Shift 2, 24 Jun 2022, Shift 2.
Same topic
Other ideas in Rolle's Theorem
Rolle's Theorem has 5 ideas JEE Main has asked; 2 of them came up in more than one question.
- Higher-Order Derivative Roots4× · 2024
- Auxiliary Functions: Product and Quotient Rulesonce · 2022
- Parameter Evaluationonce · 2021
- Logarithmic Function Applicationonce · 2020