Quadratic Equation - JEE Main Previous Year Question with Solutions

JEE Main typically has 1 to 3 questions from Quadratic Equations per session. Based on NTA papers from 2019 to 2024, the chapter has appeared in every single session. Across both January and April sessions, this chapter contributes approximately 8–12 marks per exam year, making it one of the highest-return chapters in JEE Main Mathematics.

Quadratic Equations is a Class 11 topic under the NTA JEE Main syllabus (Algebra unit). It builds on Class 10 concepts. However, its applications appear in Class 12 topics like Complex Numbers, Matrices, and Calculus, so a strong foundation in Class 11 directly supports performance across multiple JEE Main chapters.

The most important sub-topics are: nature of roots and discriminant conditions, sum and product of roots (Vieta's formulas), range of quadratic expressions, and common roots between two equations. Together, these four sub-topics account for over 80% of all JEE Main questions from this chapter based on past papers.

PYQs are necessary but not sufficient on their own. You should first understand the core theory (from NCERT or class notes), then practise PYQs to recognise NTA's question patterns, then attempt fresh mock questions to ensure you can handle unseen variations. PYQs give you pattern recognition; fresh problems test true understanding.

When an equation involves (–1) raised to a variable power, the expression equals +1 only if the exponent is even. If x = 3 makes the exponent odd, then (–1)³ = –1, which does not satisfy the equation. Such values are called extraneous solutions — they arise from algebraic manipulation but do not satisfy the original equation. Always verify solutions in the original equation.

Write Vieta's relations (α + β and αβ) immediately after reading the question, even before identifying what is being asked. This single habit eliminates the most common time-wasting step. Also, memorise the standard results for α² + β², α³ + β³, and (α – β)² in terms of sum and product, so you are not deriving them under time pressure.