JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 September 2020, Shift 2, Maths Q52

Question 52 of 75 in this shift, Maths question 2 of 25.

\alpha

and

\beta

are the roots of the equation

2x(2x+1)=1

, then

\beta

is equal to :

(1) $2\alpha(\alpha+1)$
(2) $-2\alpha(\alpha+1)$ Official answer
(3) $2\alpha^2$
(4) $2\alpha(\alpha-1)$

Official answer

Option 2

NTA final key (Sep 2020).

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

Same idea in other shifts

Asked 8× in all

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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
28 Jul 2022, Shift 1 · Q30The sum of all real values of $x$ for which $\frac{3x^2-9x+17}{x^2+3x+10}=\frac{5x^2-7x+19}{3x^2+5x+12}$ is equal to __________.MediumNumerical value

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.