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Maths · Class 11 · Complex Numbers and Quadratic Equations

Quadratic Equations for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Roots and coefficients, nature of roots, common roots, location of roots and quadratic inequalities.

Roots and coefficients, nature of roots, common roots, location of roots and quadratic inequalities.

Key ideas

Quadratic Equations: what you must understand

  • D > 0 real distinct, D = 0 equal, D < 0 complex
  • Sum of roots −b/a, product c/a
  • Graph opens up if a > 0
  • Location of roots uses D, f(k) and the vertex
Formula sheet

Must-know formulas for Quadratic Equations

  • x = (−b ± √D)/2a, D = b² − 4ac
  • Equation with roots α, β: x² − (α+β)x + αβ = 0
  • α² + β² = (α+β)² − 2αβ
  • Common root condition: (c₁a₂ − c₂a₁)² = (b₁c₂ − b₂c₁)(a₁b₂ − a₂b₁)
Print

One-page formula sheet

Printable Quadratic Equations formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

  • Ignoring a = 0 case
  • Forgetting conditions for both roots on one side of k
  • Sign errors in symmetric expressions
For the exam

How this topic is asked in JEE

Appears frequently. Usually combined with complex numbers or inequalities. Practise symmetric functions of roots.

NCERT map

Where Quadratic Equations is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

ClassBookChapterSections JEE asks from
Class 11MathematicsComplex Numbers and Quadratic EquationsQuadratic Equations; Algebra of Complex Numbers; The Modulus and the Conjugate of a Complex Number
JEE Advanced level

A JEE Advanced-level example on Quadratic Equations

Question. If the quadratic equations x² + ax + b = 0 and x² + bx + a = 0 have exactly one common root, and a ≠ b, find all possible values of (a + b).

Show solution
  1. Let α be the common root. Then α² + aα + b = 0 and α² + bα + a = 0.
  2. Subtract the two equations: (a − b)α − (a − b) = 0, which gives (a − b)(α − 1) = 0.
  3. Since a ≠ b, we must have α = 1.
  4. Substitute α = 1 into the first equation: 1 + a + b = 0, so a + b = −1.
  5. Verify: with a + b = −1, both equations are satisfied when x = 1, and since a ≠ b the equations are not identical, confirming exactly one common root.

Answer: a + b = −1

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Quadratic Equations

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

Practise

Where to practise for free

FAQs

Frequently asked questions

Is Quadratic Equations important for JEE Main 2027?

Appears frequently. It is part of the official 'Complex Numbers and Quadratic Equations' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Quadratic Equations?

x = (−b ± √D)/2a, D = b² − 4ac; Equation with roots α, β: x² − (α+β)x + αβ = 0; α² + β² = (α+β)² − 2αβ.

How should I study Quadratic Equations for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Usually combined with complex numbers or inequalities. Practise symmetric functions of roots.

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