JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 4 August 2021, Shift 2, Maths Q82

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

The integral value of

a

, for which the equation

(x^2+x+2)^2-(a-3)(x^2+x+2)(x^2+x+1)+(a-4)(x^2+x+1)^2=0

has real roots, is ________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Resolution into Two Linear Factors

Same topic in other shifts

All Quadratic Roots questions

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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.