About Quadratic Equations

A quadratic equation \( ax^2 + bx + c = 0 \) is solved using the quadratic formula:

• \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

The discriminant \( \Delta = b^2 - 4ac \) determines the nature of the roots: positive for two real roots, zero for one real root, and negative for complex roots. For example, \( x^2 - 5x + 6 = 0 \) has roots 2 and 3.