Equal roots occur in a quadratic equation when the discriminant equals zero. This means both roots have the same value indicating the parabola touches the x-axis at exactly one point. For example x² + 4x + 4 = 0 has equal roots of -2 and -2.

A quadratic equation has the standard form ax² + bx + c = 0 where a b and c are real numbers and a ≠ 0. Every quadratic equation has two roots that can be found using the quadratic formula: x = [-b ± √(b² – 4ac)]/2a. The term b² – 4ac is called the discriminant and determines the nature of roots. When discriminant equals zero the equation has equal roots. For real roots the discriminant must be greater than or equal to zero.