JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Let

\alpha,\beta,\gamma

be the three roots of the equation

x^3+bx+c=0

. If

\beta\gamma=1=-\alpha

, then

b^3+2c^3-3\alpha^3-6\beta^3-8\gamma^3

is equal to

(1) $\frac{169}{8}$
(2) $\frac{155}{8}$
(3) $19$ Official answer
(4) $21$

Official answer

Option 3

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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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
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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

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.