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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Both Roots Positive

JEE Main asked Both Roots Positive 2 times in 2 of the 108 shifts Lumi analysed, in 2025 and 2026. It belongs to Location of Roots, in Complex Numbers and Quadratic Equations (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
2025
last in 2026
Pattern
New since 2024
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200’210’220’230’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Count integer parameters for root condition
  • Parameter range for both roots positive

Difficulty

Easy 0Medium 2Hard 0

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.

  1. 4 Apr 2026, Shift 2 · Q5If the quadratic equation (λ+2)x2−3λx+4λ=0(\lambda+2)x^2-3\lambda x+4\lambda=0, λ≠−2\lambda\neq-2, has two positive roots, then the number of possible…MediumSingle correct
  2. 2 Apr 2025, Shift 2 · Q21If the set of all a∈R−{1}a \in \mathbf{R} - \{1\}, for which the roots of the equation (1−a)x2+2(a−3)x+9=0(1-a)x^2 + 2(a-3)x + 9 = 0 are positive is…MediumNumerical value

Shifts: 2 Apr 2025, Shift 2, 4 Apr 2026, Shift 2.

Same topic

Other ideas in Location of Roots

Location of Roots has 5 ideas JEE Main has asked; 1 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas