1. Introduction to Quadratic Equations
A quadratic equation is a polynomial equation of degree 2. It's fundamental in algebra and appears frequently in JEE Mathematics.
General Form
ax² + bx + c = 0
where a, b, c are real numbers and a ≠ 0
📝 Examples:
- x² - 5x + 6 = 0
- 2x² + 3x - 1 = 0
- x² - 4 = 0
2. Solution Methods
Factorization
Example: x² - 5x + 6 = 0
Solution: (x - 2)(x - 3) = 0 → x = 2 or x = 3
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
3. The Discriminant
Discriminant (Δ)
Δ = b² - 4ac
Δ > 0
Two distinct real roots
Δ = 0
One repeated real root
Δ < 0
Two complex roots
4. Applications
Projectile Motion
Height equation: h(t) = -5t² + 20t + 5
Find when ball hits ground (h = 0)
5. Practice Problems
Problem 1
Solve: x² - 6x + 8 = 0