5, Using complex numbers you will always get 5 roots.
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It can have 1, 2 or 3 unique roots.
A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021
According to the rational root theorem, which of the following are possible roots of the polynomial function below?F(x) = 8x3 - 3x2 + 5x+ 15
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
Such an equation has a total of six roots; the number of real roots must needs be even. Thus, depending on the specific equation, the number of real roots may be zero, two, four, or six.