JEE Main 2024 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 29 January 2024, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Let

\alpha,\beta

be the roots of the equation

x^2-x+2=0

with

Im(\alpha)>Im(\beta)

. Then

\alpha^6+\alpha^4+\beta^4-5\alpha^2

is equal to ______.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Higher Degree Evaluation via Root Substitution

Same topic in other shifts

All Quadratic Roots questions

2 Apr 2026, Shift 1 · Q1Let $\alpha, \alpha+2, \alpha \in \mathbb{Z}$ , be the roots of the quadratic equation…HardSingle correct
2 Apr 2026, Shift 1 · Q23Let $a, b, c \in \{1, 2, 3, 4\}$ . If the probability, that $ax^2+2\sqrt2\,bx+c>0$ for all $x \in \mathbf{R}$ , is $\frac{m}{n}$ ,…MediumNumerical value
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 42 of the 174 JEE Main shifts held from 2017 to 2026.