JEE Main 2022 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 30 July 2022, Shift 2, Maths Q83

Question 83 of 90 in this shift, Maths question 23 of 30, Section B.

The number of integral values of

b

for which

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

has three distinct real roots 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

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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
27 Jun 2022, Shift 1 · Q6The number of distinct real roots of $x^4-4x+1=0$ is :MediumSingle correct
27 Aug 2021, Shift 1 · Q85The number of distinct real roots of the equation $3x^4+4x^3-12x^2+4=0$ is __________.MediumNumerical value
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.