Learn

Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Common Root Condition

JEE Main asked Common Root Condition 5 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021 and 2022. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 1 year. In 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
3 of 8
First asked
2020
last in 2022
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021 and 2022. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.07’210.07’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 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.

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20222 of 24
  • 20212 of 24
  • 20201 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.

  • Value from roots of linked quadratics

Difficulty

Easy 1Medium 2Hard 2

3 of the 5 questions had a numerical answer.

Every question

All 5 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 26 Jul 2022, Shift 1 · Q21If for some p, q, r∈R\mathrm{p},\ \mathrm{q},\ \mathrm{r} \in \mathbf{R}, not all have same sign, one of the roots of the equation…HardNumerical value
  2. 25 Jul 2022, Shift 2 · Q22Let f(x)f(x) be a quadratic polynomial with leading coefficient 1 such that f(0)=p,p≠0f(0)=p,p\neq0, and f(1)=13f(1)=\frac{1}{3}. If the equations…HardNumerical value
  3. 26 Aug 2021, Shift 2 · Q81Let λ≠0\lambda\neq0 be in R\mathbf{R}. If α\alpha and β\beta are the roots of the equation x2−x+2λ=0x^2-x+2\lambda=0, and α\alpha and γ\gamma…MediumNumerical value
  4. 3 Aug 2021, Shift 2 · Q62If the equations 2x2+kx−5=02x^2 + kx - 5 = 0 and x2−3x−4=0x^2 - 3x - 4 = 0 have one root in common, then a value of 'kk' isEasySingle correct
  5. 9 Jan 2020, Shift 2 · Q52Let a,b∈Ra,b\in\mathbf{R}, a≠0a\ne0 be such that the equation, ax2−2bx+5=0ax^2-2bx+5=0 has a repeated root α\alpha, which is also a root of the…MediumSingle correct

Shifts: 9 Jan 2020, Shift 2, 3 Aug 2021, Shift 2, 26 Aug 2021, Shift 2, 25 Jul 2022, Shift 2, 26 Jul 2022, Shift 1.

Same topic

Other ideas in Quadratic Roots

Quadratic Roots has 22 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas