f (x) has two real roots and one imaginary root.f (x) has three real roots.f (x) has five real roots.f (x) has three real roots and two imaginary roots.
Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29).
Use the fundamental theorem of algebra and the complex conjugate theorem to determine the number and nature of the remaining root(s). Explain your thinking.
The polynomial is degree 3, so it has three roots counting multiplicity. Two roots are given, leaving one remaining root. If the given roots are non-real complex conjugates, the remaining root must be real, since non-real roots occur in conjugate pairs.
Did you include the following in your response?
Did you find these answers helpful?