3. How is the Fundamental Theorem of Algebra true for quadratic polynomials?

Step-by-step explanation:

Theorm-The Fundamental Theorem of Algebra: If P (x) is a polynomial of degree n ≥ 1, then P (x) = 0 has exactly n roots, including multiple and complex roots.

Let's verify that the Fundamental Theorem of Algebra holds for quadratic polynomials.

A quadratic polynomial is a second degree polynomial. According to the Fundamental Theorem of Algebra, the quadratic set = 0 has exactly two roots.

As we have seen, factoring a quadratic equation will result in one of three possible situations.

graph 1

The quadratic may have 2 distinct real roots. This graph crosses the

x-axis in two locations. These graphs may open upward or downward.

graph 2

It may appear that the quadratic has only one real root. But, it actually has one repeated root. This graph is tangent to the x-axis in one location (touching once).

graph 3

The quadratic may have two non-real complex roots called a conjugate pair. This graph will not cross or touch the x-axis, but it will have two roots.