JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 3 August 2021, Shift 1, Maths Q82

Question 82 of 90 in this shift, Maths question 22 of 30, Section B.

The sum of modulus of all non-real roots of the equation,

(x^2 + 4x + 6)(2x^2 + 8x + 14) = 12

is equal to ______ .

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Reducible Biquadratics

Same topic in other shifts

All Quadratic Roots questions

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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
2 Apr 2026, Shift 2 · Q12Let the parabola $y = x^2 + px + q$ passing through the point $(1, -1)$ be such that the distance between its vertex and the $x$ -axis is…MediumSingle correct
4 Apr 2026, Shift 2 · Q2Let $S=\{z\in\mathbb{C}:z^2+4z+16=0\}$ . Then $\sum_{z\in S}|z+\sqrt{3}\,i|^2$ is equal to:EasySingle correct
4 Apr 2026, Shift 2 · Q4If $\alpha=1$ and $\beta=1+i\sqrt{2}$ , where $i=\sqrt{-1}$ are two roots of the equation $x^3+ax^2+bx+c=0$ , $a,b,c\in\mathbb{R}$ , then…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.