JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 1 February 2024, Shift 2, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

Let

\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 non constant G.P. and

\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}

, then the value of

(\alpha-\beta)^2

is :

(1) $9$
(2) $\frac{80}{9}$ Official answer
(3) $\frac{20}{3}$
(4) $8$

Official answer

Option 2

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

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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
6 Apr 2024, Shift 1 · Q21Let $x_1, x_2, x_3, x_4$ be the solution of the equation $4x^4+8x^3-17x^2-12x+9=0$ and…HardNumerical value
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.