= x^5 + 3x^3 − 4
This function has at least one real root:
x = 1 ----> y(1) = 0
Since this is a 5th degree polynomial, it has at most 5 unique roots, and since we know at least 1 is real, then it must have at most 4 unique complex roots.
Since the choices are 4, 5, 6, then answer can only be: 4
------------------------------
NOTE: x-intercepts are real zeros or roots
The graphs of a polynomial function of degree 5 has three x-intercepts, all with multiplicity 1.
A 5th degree polynomial will have 5 roots (counting multiplicities)
Since this function has 3 x-intercepts, then it has 3 real roots, and 2 complex roots
------------------------------
The polynomial function y = x^3 − 3x^2 + 16x − 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
This is a 3rd degree polynomial, so it has 3 roots (counting multiplicities).
Since it has only one non-repeated (i.e. multiplicity = 1) x-intercept, then it has 1 real root and 2 complex roots.
