ax² + bx + c = 0
Solution Steps:
Discriminant (Δ) = ...
Nature: ...
x = ...
The Quadratic Formula Explained
A quadratic equation is a polynomial equation of degree 2, usually written as ax² + bx + c = 0. To find the values of x (the roots), we use the universal quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
Understanding the Discriminant (Δ)
The part under the square root, b² - 4ac, is called the Discriminant. It tells us about the nature of the roots:
- Δ > 0: Two distinct real roots.
- Δ = 0: One real root (repeated).
- Δ < 0: No real roots (Complex/Imaginary numbers).