Question

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

Answer 1

Answer:

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.