After solving the equation x^2+ 9 = 6x, Donna stated that the Fundamental Theorem of Algebra is true for this equation. However,
Cassie stated that the Fundamental Theorem of Algebra is NOT true for this equation. Which statement justifies a correct conclusion about the Fundamental Theorem of Algebra with
respect to the given equation?
A Donna is correct because there is a double root.
B. Cassie is correct because there are no real roots.
C. Cassie is correct because there is only one real root
D. Donna is correct because there are two different real roots.
The Fundamental Theorem of Algebra states that the number of complex roots a polyomial has is equal to its highest exponent. This is a squared polynomial; second degree; quadratic. When it is factored, no matter what types of numbers you get as the solution, you will ALWAYS have 2 of them. When this quadratic is factored, we get that x = 3 and x = 3. That means that this is a quadratic that touches the x-axis at (3, 0). It doesn't go through, it only touches. We do have 2 roots, but since they're the same, we say we have a multiplicity 2 of that root. The closest you'll come to that in your choices is A. Apparently your text refers to multiplicity 2 as a double root.
