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JEE Advanced Quadratic Equations questions with solutions

Roots, nature of roots, discriminant and inequalities. 12 questions from our 2016–2024 JEE Advanced pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Quadratic Equations for JEE Main · Quadratic Equations for CAT · Quadratic Equations for NDA

JEE Advanced 2024

Then (1)/(2-α^2+(1)/(2-β^2+(1)/(2-γ^2 equalsJEE Advanced 2024 Paper 1 · hard
Let α,β,γ be the roots of x^3-3x+1=0. Which of the following is/are correct?JEE Advanced 2024 Paper 2 · medium

JEE Advanced 2022

Find the value of (1)/(α^2+1)+(1)/(β^2+1)+(1)/(γ^2+1).JEE Advanced 2022 Paper 1 · medium
Let x,y,z be real numbers with x+y+z=4 and x^2+y^2+z^2=6. Let M and m be the greatest and the least possible values of the product xyz. Find M-m.JEE Advanced 2022 Paper 1 · hard
For a real number k, let p(x)=x^3-3x+k with roots a,b,c (counted with multiplicity).JEE Advanced 2022 Paper 2 · medium

JEE Advanced 2021

Let f(x)=x^3-3x. The number of distinct real solutions of f(f(x))=0 isJEE Advanced 2021 Paper 2 · hard

JEE Advanced 2020

Let a,b,c be the roots of x^3-3x+1=0.JEE Advanced 2020 Paper 1 · hard

JEE Advanced 2019

Let α,β,γ be the roots of x^3-3x+1=0. Which of the following statements is/are correct?JEE Advanced 2019 Paper 1 · hard

JEE Advanced 2017

The value of (α^2/(βγ)+(β^2/(γα)+(γ^2/(αβ) isJEE Advanced 2017 Paper 2 · medium

JEE Advanced 2016

Let α,β,γ be the roots of x^3-2x^2+3x-5=0. Which of the following is/are correct?JEE Advanced 2016 Paper 1 · medium
Let g(x)=x^3-6x^2+9x-2. The number of distinct real solutions of the equation |g(x)|=1 isJEE Advanced 2016 Paper 1 · medium
Consider the cubic equation x^3-6x^2+9x-k=0, where k is a real constant.JEE Advanced 2016 Paper 2 · medium

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9