Theorem of Bezout

The Bézout's Theorem states that for any two polynomial equations, the maximum number of points where their graphs intersect (considering complex solutions and counting multiplicities) is equal to the product of their degrees—meaning, if one is quadratic (degree 2) and the other cubic (degree 3), they can intersect in up to six points. This theorem provides a fundamental rule for understanding the intersection behavior of algebraic curves, ensuring that, under certain conditions, the maximum number of intersections is predictable and tied directly to the degrees of the polynomials involved.