JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

\alpha, \beta

be the roots of the equation

x^2-4\lambda x+5=0

and

\alpha, \gamma

be the roots of the equation

x^2-\left(3\sqrt{2}+2\sqrt{3}\right)x+7+3\lambda\sqrt{3}=0

\lambda>0

. If

\beta+\gamma=3\sqrt{2}

, then

(\alpha+2\beta+\gamma)^2

is equal to ___________.

Official answer

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
29 Jun 2022, Shift 1 · Q8Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + (2i - 1) = 0$ . Then, the value of $|\alpha^8 + \beta^8|$ 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 108 of the 174 JEE Main shifts held from 2017 to 2026.