JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 6 April 2024, Shift 1, Maths Q21

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

Let

x_1, x_2, x_3, x_4

be the solution of the equation

4x^4+8x^3-17x^2-12x+9=0

and

\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16}m

. Then the value of

m

is __________

Official answer

221

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Root-Coefficient Relation

Same idea in other shifts

Asked 15× in all

2 Apr 2026, Shift 1 · Q1Let $\alpha, \alpha+2, \alpha \in \mathbb{Z}$ , be the roots of the quadratic equation…HardSingle correct
5 Apr 2026, Shift 1 · Q1Let $a, b \in \mathbb{C}$ . Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$ . If $\beta - \alpha = \sqrt{11}$ and…MediumSingle correct
5 Apr 2026, Shift 2 · Q1Let $\alpha, \beta$ be the roots of the equation $x^2-x+p=0$ and $\gamma, \delta$ be the roots the equation $x^2-4x+q=0$ ;…MediumSingle correct
5 Apr 2026, Shift 2 · Q2Let $z_1, z_2 \in \mathbb{C}$ be the distinct solutions of the equation $z^2+4z-(1+12i)=0$ . Then $|z_1|^2+|z_2|^2$ is equal to :MediumSingle correct
6 Apr 2026, Shift 2 · Q2Consider the quadratic equation $(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0$ , $n\in\mathbf{R}$ . Let $\alpha$ be the minimum value of the product of…MediumSingle correct
3 Apr 2025, Shift 2 · Q4Let the equation $x(x + 2)(12 - k) = 2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line…EasySingle correct
1 Feb 2024, Shift 2 · Q4Let $\alpha$ and $\beta$ be the roots of the equation $px^2+qx-r=0$ , where $p\neq 0$ . If $p$ , $q$ and $r$ be the consecutive terms of a…MediumSingle correct
8 Apr 2023, Shift 1 · Q3Let $\alpha,\beta,\gamma$ be the three roots of the equation $x^3+bx+c=0$ . If $\beta\gamma=1=-\alpha$ , 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.