Equal roots occur when the discriminant (b² – 4ac) equals zero in a quadratic equation. This makes both roots identical meaning the parabola touches the x-axis at exactly one point. The value of both roots can be found using -b/2a and this point is called the vertex of the parabola.

A quadratic equation takes the form ax² + bx + c = 0 where a is not equal to zero. These equations have vital applications in physics business and engineering. The solutions or roots can be found using factorization methods perfect square method or quadratic formula (-b ± √(b² – 4ac))/2a.
A quadratic equation can have real and distinct roots real and equal roots or no real roots based on the discriminant (b² – 4ac). Understanding graphical representation helps visualize the nature of roots as intersections with x-axis.