JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2026, Shift 1, Maths Q1

Question 1 of 75 in this shift, Maths question 1 of 25, Section A.

Let

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

\beta^2 - \alpha^2 = 3i\sqrt{11}

, then

(\beta^3 - \alpha^3)^2

is equal to:

(1)160
(2)176Official answer
(3)194
(4)187

Official answer

Option 2

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Root-Coefficient Relation

Same idea in other shifts

Asked 8× in all

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 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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.