JEE Main 2021 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 27 August 2021, Shift 1, Maths Q85

Question 85 of 90 in this shift, Maths question 25 of 30, Section B.

The number of distinct real roots of the equation

3x^4+4x^3-12x^2+4=0

is __________.

Official answer

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Analyzing Polynomial Roots via Extrema

Same idea in other shifts

Asked 6× in all

4 Apr 2025, Shift 2 · Q16Let $f$ be a differentiable function on $\mathbf{R}$ such that $f(2)=1$ , $f'(2)=4$ . Let…HardSingle correct
26 Jul 2022, Shift 1 · Q24The number of distinct real roots of the equation $x^5(x^3 - x^2 - x + 1) + x\ (3x^3 - 4x^2 - 2x + 4) - 1 = 0$ is ___________.HardNumerical value
30 Jul 2022, Shift 2 · Q83The number of integral values of $b$ for which $2x^3 - 3x^2 - 12x + b = 0$ has three distinct real roots is ________.MediumNumerical value
27 Jun 2022, Shift 1 · Q6The number of distinct real roots of $x^4-4x+1=0$ is :MediumSingle correct
3 Sep 2020, Shift 2 · Q58Suppose $f(x)$ is a polynomial of degree four, having critical points at $-1$ , 0, 1. If $T = \{x \in \mathbf{R} \mid f(x) = f(0)\}$ , 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.