8
CBSE Marks
★★★★★
Difficulty
9
Topics
Very High
Board Weight
Topics Covered
9 key topics in this chapter
Standard Form ax²+bx+c=0
Solutions by Factorisation
Completing the Square
Quadratic Formula
Discriminant: Nature of Roots
D>0: Two Distinct Real Roots
D=0: Equal Real Roots
D<0: No Real Roots
Word Problems & Applications
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Quadratic Formula | \(x = \dfrac{−b ± \sqrt{b²−4ac}}{2a}\) |
| Discriminant | \(D = b² − 4ac\) |
| D > 0 | \(\text{Two distinct real roots}\) |
| D = 0 | \(\text{Two equal real roots: x = −b/2a}\) |
| D < 0 | \(\text{No real roots}\) |
| Sum of roots | \(α + β = −b/a\) |
| Product of roots | \(αβ = c/a\) |
Important Points to Remember
A quadratic equation has real roots if and only if the discriminant D = b²−4ac ≥ 0.
When D > 0: two distinct real roots. D = 0: two equal (coincident) real roots. D < 0: no real roots.
Completing the square is the method used to derive the quadratic formula.
Word problems: read carefully, define variables, form the equation, solve, and verify.