JEE Main Maths · Complex Numbers and Quadratic Equations

Root-Coefficient Relation

Root-Coefficient Relation (Complex Numbers and Quadratic Equations) was asked 8 times in 7 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed. 1 of the 8 had a numerical answer.

Times asked: 8; in 7 shifts
Years: 2020–2026
Usual format: Single correct; Multi-step
Pattern: Frequent; repeats across shifts

How it is asked

Unknown from roots of summed-product quadratic
Expression from root differences of quadratic

Difficulty

Easy 1Medium 6Hard 1

Where it sits

Chapter: Complex Numbers and Quadratic Equations. Topic: Quadratic Roots, 46 questions over 19 ideas.

All 8 questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q1Let $\alpha, \alpha+2, \alpha \in \mathbb{Z}$ , be the roots of the quadratic equation…HardSingle correct
5 Apr 2026, Shift 1 · Q1Let $a, b \in \mathbb{C}$ . Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$ . If $\beta - \alpha = \sqrt{11}$ and…MediumSingle correct
5 Apr 2026, Shift 2 · Q1Let $\alpha, \beta$ be the roots of the equation $x^2-x+p=0$ and $\gamma, \delta$ be the roots the equation $x^2-4x+q=0$ ;…MediumSingle correct
5 Apr 2026, Shift 2 · Q2Let $z_1, z_2 \in \mathbb{C}$ be the distinct solutions of the equation $z^2+4z-(1+12i)=0$ . Then $|z_1|^2+|z_2|^2$ is equal to :MediumSingle correct
6 Apr 2026, Shift 2 · Q2Consider the quadratic equation $(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0$ , $n\in\mathbf{R}$ . Let $\alpha$ be the minimum value of the product of…MediumSingle correct
3 Apr 2025, Shift 2 · Q4Let the equation $x(x + 2)(12 - k) = 2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line…EasySingle correct
28 Jul 2022, Shift 1 · Q30The sum of all real values of $x$ for which $\frac{3x^2-9x+17}{x^2+3x+10}=\frac{5x^2-7x+19}{3x^2+5x+12}$ is equal to __________.MediumNumerical value
6 Sep 2020, Shift 2 · Q52If $\alpha$ and $\beta$ are the roots of the equation $2x(2x+1)=1$ , then $\beta$ is equal to :MediumSingle correct