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JEE Main Quadratic Equations questions with solutions

Roots, nature of roots, discriminant and inequalities. 9 questions from our 2016–2025 JEE Main pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

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

JEE Main 2025

Let α>β be the roots of x^2-6x-2=0 and an=α^n+β^n. Then (a10-2a8)/(2a9) equalsJEE Main 2025 · medium

JEE Main 2024

Let m be real. Both roots of x^2-2mx+m^2-4=0 lie strictly inside the interval (-1,7) exactly when p<m<q. The value of q-p isJEE Main 2024 · medium

JEE Main 2023

The sum of all integers x satisfying ((x-2)(x-5))/((x+1)(x-4))≤ 0 isJEE Main 2023 · medium

JEE Main 2022

If α,β are the roots of x^2-3x-5=0, then the quadratic equation whose roots are α+(1)/(β) and β+(1)/(α) isJEE Main 2022 · medium

JEE Main 2021

The number of integer values of m for which both roots of x^2-2mx+m^2-1=0 lie strictly between -2 and 4 isJEE Main 2021 · medium

JEE Main 2019

The number of integer values of k in the interval [-10,10] for which x^2+kx+4=0 has real roots isJEE Main 2019 · medium

JEE Main 2018

The equations x^2+px+q=0 and x^2+qx+p=0 with p≠ q have exactly one common root. If the two non-common roots differ by 4 in absolute value, then 4pq…JEE Main 2018 · medium

JEE Main 2017

If the equations x^2+ax+12=0, x^2+bx+15=0 and x^2+(a+b)x+36=0 have a common root, then ab equalsJEE Main 2017 · hard

JEE Main 2016

The number of integer values of m for which both roots of x^2-(m+1)x+(m^2-2)=0 are real and positive isJEE Main 2016 · hard

Other Mathematics topics

Area Under Curves 7 Binomial Theorem 12 Complex Numbers 10 Conic Sections 5 Differential Equations 9 Differentiation and Application of Derivatives 19 Indefinite and Definite Integrals 16 Limits 9 Matrices and Determinants 19 Permutations and Combinations 10 Probability 9 Sequences and Series 9 Sets, Relations and Functions 10 Statistics 6 Straight Lines and Circles 9 Three Dimensional Geometry 14 Trigonometry and Inverse Trigonometric Functions 9 Vector Algebra 8