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Mathematics

The Quadratic Formula and the Nature of Roots

Quick fact

The quadratic formula was known to ancient Babylonians over 4,000 years ago, and the discriminant—the part under the square root—tells you exactly whether the solutions are real or complex without solving the equation.

Why this is interesting

You’ve probably memorized the quadratic formula, but have you ever wondered why it always works—or why it sometimes gives you a square root of a negative number?