Concept Topic GuideCBSE & ICSEClass 10MathematicsChapter 4Verified Faculty Notes & Solutions
Quadratic Equations Class 10 – Discriminant, Roots & NCERT Formulas
Master Class 10 Mathematics Quadratic Equations: Quadratic formula (Sridharacharya), nature of roots, factorization method, and board exam word problems.
7 students readUpdated 30 August 2026
Quadratic Equations – Complete Concept Guide & Formulas
A quadratic equation in variable x is an algebraic equation of the second degree of the standard form: ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.
Table of Contents
Standard Form & Methods of Solving
- Factorization (Splitting the Middle Term): Express
ax² + bx + c = 0as(x - α)(x - β) = 0. - Quadratic Formula: Direct mathematical calculation for real/irrational roots.
The Quadratic Formula
x = [ -b ± √(b² - 4ac) ] / (2a)Where the quantity D = b² - 4ac is termed the Discriminant.
The Discriminant & Nature of Roots
| Discriminant Value (D = b² - 4ac) | Nature of Roots | Graphical Representation |
|---|---|---|
| D > 0 | Two distinct real roots: α ≠ β | Parabola intersects x-axis at 2 distinct points |
| D = 0 | Two equal real roots: α = β = -b / (2a) | Parabola touches x-axis at exactly 1 point (tangent) |
| D < 0 | No real roots (Imaginary / Complex conjugate roots) | Parabola does not intersect or touch x-axis |
Indexed Topics & Examination Keywords
#CBSE Class 10 Maths#ICSE Class 10 Maths#Quadratic Equations#Nature of Roots#Discriminant Formula#NCERT Solutions#Board Exam 2026#RD Sharma Maths
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