How do you find the number of roots for #x^3 - 3x^2 - 18x - 176 = 0# using the fundamental theorem of algebra?

1 Answer
Apr 5, 2016

Since the function's degree is #3#, it has #3# roots.

Explanation:

The Fundamental Theorem of Algebra (FTOA), for a polynomial function such as #x^3-3x^2-18x-176=0#, states that the degree of the polynomial function is equivalent to the function's number of roots.

The degree of a function is the highest exponent on any of its terms, which in this case is the #3# in the exponent of #x^3#.

Since this function has degree #3#, the FTOA states that it will have three roots.

graph{x^3-3x^2-18x-176 [-10, 15, -300, 70]}

Graphing the function, it appears to have only one root (zero) at #x=8#, but it has #2# more complex roots for a total of #3# roots.