JEE Main Maths · Complex Numbers and Quadratic Equations

Roots of Modulus Quadratics

Roots of Modulus Quadratics (Complex Numbers and Quadratic Equations) was asked 3 times in 3 JEE Main shifts, 2023–2025, out of the 42 shifts Lumi analysed. 2 of the 3 had a numerical answer.

Times asked: 3; in 3 shifts
Years: 2023–2025
Usual format: Numerical value; Multi-step
Pattern: Comes in cycles; repeats across shifts

How it is asked

Value from roots of linked quadratics
Number of real roots of modulus equation

Difficulty

Easy 0Medium 2Hard 1

Where it sits

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

All 3 questions

Newest first, each with its options and official answer.

8 Apr 2025, Shift 2 · Q2The sum of the squares of the roots of $|x-2|^2 + |x-2| - 2 = 0$ and the squares of the roots of $x^2 - 2|x-3| - 5 = 0$ , isMediumSingle correct
30 Jan 2024, Shift 2 · Q22The number of real solutions of the equation $x\left(x^2 + 3|x| + 5|x-1| + 6|x-2|\right) = 0$ is ________.MediumNumerical value
8 Apr 2023, Shift 2 · Q22Let $m$ and $n$ be the numbers of real roots of the quadratic equations $x^2 - 12x + [x] + 31 = 0$ and $x^2 - 5|x + 2| - 4 = 0$ …HardNumerical value