JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Let S be the set of all integral values of

\alpha

for which the sum of squares of two real roots of the quadratic equation

3x^2 + (\alpha-6)x + (\alpha+3) = 0

is minimum. Then S :

(1)is an empty setOfficial answer
(2)is a singleton
(3)contains exactly two elements
(4)contains more than two elements

Official answer

Option 1

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Symmetric Functions

Same idea in other shifts

Asked 12× in all

2 Apr 2026, Shift 2 · Q1Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$ , and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation…MediumSingle correct
3 Apr 2025, Shift 1 · Q4Let $z \in \mathbb{C}$ be such that $\frac{z^2 + 3i}{z - 2 + i} = 2 + 3i$ . Then the sum of all possible values of $z^2$ isMediumSingle correct
31 Jan 2024, Shift 2 · Q3Let $z_1$ and $z_2$ be two complex numbers such that $z_1+z_2=5$ and $z_1^3+z_2^3=20+15i$ . Then, $|z_1^4+z_2^4|$ equals -HardSingle correct
26 Jul 2022, Shift 2 · Q1The minimum value of the sum of the squares of the roots of $x^2+(3-a)x+1=2a$ is:EasySingle correct
24 Jun 2022, Shift 1 · Q7If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^2+\lambda x-1=0$ is 15, then…MediumSingle correct
25 Jun 2022, Shift 2 · Q2Let $a, b \in \mathbb{R}$ be such that the equation $ax^2 - 2bx + 15 = 0$ has a repeated root $\alpha$ . If $\alpha$ and $\beta$ are the…MediumSingle correct
26 Jun 2022, Shift 2 · Q22Let $p$ and $q$ be two real numbers such that $p + q = 3$ and $p^4 + q^4 = 369$ . Then $\left(\frac{1}{p} + \frac{1}{q}\right)^{-2}$ is…MediumNumerical value
27 Jun 2022, Shift 2 · Q22Let $\alpha, \beta$ be the roots of the equation $x^2-4\lambda x+5=0$ and $\alpha, \gamma$ be the roots of the equation…HardNumerical value

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 108 of the 174 JEE Main shifts held from 2017 to 2026.