JEE Main Maths · Complex Numbers and Quadratic Equations

Location of Roots in JEE Main

Name: Location of Roots: JEE Main previous year questions
Creator: Lumi

Location of Roots (Maths, Complex Numbers and Quadratic Equations) came 5 times in 5 of the 42 JEE Main shifts Lumi analysed, across 4 distinct ideas. 5 of them came in 2024–26; it was last asked in 2026.

Questions: 5; in 5 shifts
Ideas asked: 4; 1 asked more than once
Numerical answer: 1; 20% of its questions
Pattern: New since 2024; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 2Hard 2

Format

Single correct4 Q
Numerical value1 Q

Ideas inside the topic

4 ideas

Both Roots Positive2 Q
Both Roots Negative1 Q
Both roots greater than k1 Q
Both roots in interval1 Q

Where it sits

Part of Complex Numbers and Quadratic Equations, which had 79 questions in all. Location of Roots accounts for 6% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Conic Sections.

Every question

All 5 Location of Roots questions

Newest first, each with its options and official answer.

4 Apr 2026, Shift 2 · Q5If the quadratic equation $(\lambda+2)x^2-3\lambda x+4\lambda=0$ , $\lambda\neq-2$ , has two positive roots, then the number of possible…MediumSingle correct
6 Apr 2026, Shift 1 · Q3Let $e_1$ and $e_2$ be two distinct roots of the equation $x^2-ax+2=0$ . Let the sets $\{a\in\mathbb{R}: e_1$ and $e_2$ are the…HardSingle correct
6 Apr 2026, Shift 2 · Q16Let $\lim_{x\to2}\frac{(\tan(x-2))\left(rx^2+(p-2)x-2p\right)}{(x-2)^2}=5$ for some $r, p\in\mathbf{R}$ . If the set of all possible values…HardSingle correct
2 Apr 2025, Shift 2 · Q21If the set of all $a \in \mathbf{R} - \{1\}$ , for which the roots of the equation $(1-a)x^2 + 2(a-3)x + 9 = 0$ are positive is…MediumNumerical value
7 Apr 2025, Shift 1 · Q3Let the set of all values of $p \in \mathbb{R}$ , for which both the roots of the equation $x^2 - (p+2)x + (2p+9) = 0$ are negative real…EasySingle correct