Revision Notes: Class 10 Maths Chapter 4 Quadratic Equations

A fast, one-glance recap of Class 10 Maths Chapter 4 (Quadratic Equations) — for the full worked explanations, see the Solutions post. These Class 10 Mathematics Chapter 4 notes are ideal for quick revision just before exams.

Last Updated: October 24, 2026

Common Mistakes Students Make in Quadratic Equations

Revision Notes: Quadratic Equations

• Standard form: ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0
• Quadratic equation: a polynomial equation of degree 2 in one variable — always check the highest power of x survives after simplification before calling something “quadratic”
• Root/solution: a real number α is a root of ax²+bx+c=0 if aα²+bα+c = 0; a quadratic equation has at most two roots
• Method 1 — Factorisation: split the middle term bx into two terms whose coefficients multiply to give ac and add to give b, then factor by grouping; each factor set to zero gives a root
• Method 2 — Quadratic formula: x = [−b ± √(b²−4ac)] / 2a
• Discriminant: D = b² − 4ac — determines the nature of the roots without fully solving the equation
• D > 0 → two distinct real roots
• D = 0 → two equal real roots (repeated root), x = −b/2a
• D < 0 → no real roots
• Condition for equal roots: b² = 4ac (used to solve for an unknown parameter k, p, m, etc. in a given equation)
• Sum and product of roots (if roots are α, β): sum α+β = −b/a, product αβ = c/a — useful for reverse-engineering an equation from its roots: x² − (sum)x + (product) = 0
• Irrational/surd roots of a quadratic with rational coefficients always occur in conjugate pairs, e.g. if one root is p+√q, the other is p−√q
• Word problem method: define the unknown clearly (age, speed, number, side length, etc.), translate every condition in the problem into an algebraic expression, form a single quadratic equation, solve it, and always reject roots that don’t fit the real-world context (negative age, negative length, negative speed, etc.)
• Common problem patterns: consecutive integers, two-part sum/product problems, age problems (present age vs. age n years ago/hence), speed–distance–time (uniform speed changed by some amount), area/perimeter of rectangles, right-triangle side relationships (Pythagoras), and cost-of-production problems
• Checking a solution: always verify by substituting the found value(s) back into the original word conditions, not just the equation, to catch sign/setup errors

See also: Extra Questions (HOTS) | Formulas Handbook

Why This Chapter Matters

Quadratic Equations is one of the most exam-heavy chapters in the current 2026-27 CBSE Class 10 Maths syllabus, and questions from it appear regularly in board exams, from 1-mark objective questions to longer 3-5 mark descriptive questions.

Extra Quick-Recall Points

• Reciprocal-root trick: if one root is the reciprocal of the other, their product = 1, so c/a = 1, i.e. a = c.
• Know by heart: the D>0 / D=0 / D<0 classification is a near-guaranteed 1-2 mark question every year.

How to Use These Notes

These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine: read the chapter once, solve the questions using the linked Solutions, then return to this page a day or two before the exam to refresh key definitions and formulas.

Frequently Asked Questions

How can you tell how many real roots a quadratic equation has without fully solving it?
By checking the discriminant D = b^2 – 4ac: if D > 0 the equation has two distinct real roots, if D = 0 it has one repeated real root, and if D < 0 it has no real roots (only complex ones, which are outside this chapter's scope).

What is the difference between solving a quadratic by factorisation and by the quadratic formula?
Factorisation works quickly when the equation splits neatly into two rational factors, but not all quadratics factor nicely; the quadratic formula, x = [-b +/- sqrt(b^2-4ac)] / 2a, always works for any quadratic equation, making it the reliable fallback method.

What to Revise First (and Last) in This Chapter

Written by Satish

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