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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Root-Coefficient Relation

JEE Main asked Root-Coefficient Relation 15 times in 14 of the 108 shifts Lumi analysed, in 2020, 2022, 2023, 2024, 2025 and 2026. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 2 years. In 2020, 2022, 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
15
in 14 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.30.60’170.33’200’210.07’220.07’230.09’240.13’250.56’26

Raw count: 2017: 0 in 1 shift · 2020: 4 in 12 shifts · 2021: 0 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 5 in 9 shifts.

Shift by shift

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

  • 202624 of 9
  • 20251 of 8
  • 20242 of 18
  • 20231 of 12
  • 20222 of 24
  • 20210 of 24
  • 20204 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Value from roots of linked quadratics
  • Roots of two quadratics in gp

Difficulty

Easy 1Medium 12Hard 2

2 of the 15 questions had a numerical answer.

Every question

All 15 questions

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

  1. 6 Apr 2026, Shift 2 · Q2Consider the quadratic equation (n2−2n+2)x2−3x+(n2−2n+2)2=0(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0, n∈Rn\in\mathbf{R}. Let α\alpha be the minimum value of the product of…MediumSingle correct
  2. 5 Apr 2026, Shift 2 · Q1Let α,β\alpha, \beta be the roots of the equation x2−x+p=0x^2-x+p=0 and γ,δ\gamma, \delta be the roots the equation x2−4x+q=0x^2-4x+q=0;…MediumSingle correct
  3. 5 Apr 2026, Shift 2 · Q2Let z1,z2∈Cz_1, z_2 \in \mathbb{C} be the distinct solutions of the equation z2+4z−(1+12i)=0z^2+4z-(1+12i)=0. Then ∣z1∣2+∣z2∣2|z_1|^2+|z_2|^2 is equal to :MediumSingle correct
  4. 5 Apr 2026, Shift 1 · Q1Let a,b∈Ca, b \in \mathbb{C}. Let α,β\alpha, \beta be the roots of the equation x2+ax+b=0x^2 + ax + b = 0. If β−α=11\beta - \alpha = \sqrt{11} and…MediumSingle correct
  5. 2 Apr 2026, Shift 1 · Q1Let α,α+2,α∈Z\alpha, \alpha+2, \alpha \in \mathbb{Z}, be the roots of the quadratic equation…HardSingle correct
  6. 3 Apr 2025, Shift 2 · Q4Let the equation x(x+2)(12−k)=2x(x + 2)(12 - k) = 2 have equal roots. Then the distance of the point (k,k2)\left(k, \frac{k}{2}\right) from the line…EasySingle correct
  7. 1 Feb 2024, Shift 2 · Q4Let α\alpha and β\beta be the roots of the equation px2+qx−r=0px^2+qx-r=0, where p≠0p\neq 0. If pp, qq and rr be the consecutive terms of a…MediumSingle correct
  8. 6 Apr 2024, Shift 1 · Q21Let x1,x2,x3,x4x_1, x_2, x_3, x_4 be the solution of the equation 4x4+8x3−17x2−12x+9=04x^4+8x^3-17x^2-12x+9=0 and…HardNumerical value
  9. 8 Apr 2023, Shift 1 · Q3Let α,β,γ\alpha,\beta,\gamma be the three roots of the equation x3+bx+c=0x^3+bx+c=0. If βγ=1=−α\beta\gamma=1=-\alpha, then…MediumSingle correct
  10. 28 Jun 2022, Shift 2 · Q2Let f(x)f(x) be a quadratic polynomial such that f(−2)+f(3)=0f(-2)+f(3)=0. If one of the roots of f(x)=0f(x)=0 is −1-1, then the sum of the roots of…MediumSingle correct
  11. 28 Jul 2022, Shift 1 · Q30The sum of all real values of xx for which 3x2−9x+17x2+3x+10=5x2−7x+193x2+5x+12\frac{3x^2-9x+17}{x^2+3x+10}=\frac{5x^2-7x+19}{3x^2+5x+12} is equal to __________.MediumNumerical value
  12. 6 Sep 2020, Shift 2 · Q52If α\alpha and β\beta are the roots of the equation 2x(2x+1)=12x(2x+1)=1, then β\beta is equal to :MediumSingle correct
  13. 4 Sep 2020, Shift 2 · Q52Let λ≠0\lambda \neq 0 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…MediumSingle correct
  14. 4 Sep 2020, Shift 1 · Q56Let α\alpha and β\beta be the roots of x2−3x+p=0x^2 - 3x + p = 0 and γ\gamma and δ\delta be the roots of x2−6x+q=0x^2 - 6x + q = 0. If…MediumSingle correct
  15. 3 Sep 2020, Shift 1 · Q52If α\alpha and β\beta are the roots of the equation x2+px+2=0x^2+px+2=0 and 1α\frac{1}{\alpha} and 1β\frac{1}{\beta} are the roots of the…MediumSingle correct

Shifts: 3 Sep 2020, Shift 1, 4 Sep 2020, Shift 2, 4 Sep 2020, Shift 1, 6 Sep 2020, Shift 2, 28 Jun 2022, Shift 2, 28 Jul 2022, Shift 1, 8 Apr 2023, Shift 1, 1 Feb 2024, Shift 2, 6 Apr 2024, Shift 1, 3 Apr 2025, Shift 2, 2 Apr 2026, Shift 1, 5 Apr 2026, Shift 2, 5 Apr 2026, Shift 1, 6 Apr 2026, Shift 2.

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