Question

How many complex roots does the polynomial equation below have? x^5 - 3 = 0

Answer 1

For any polynomial equation, The Fundamental Theorem of Algebra tells you that the highest degree present will tell you how many complex roots the equation has. There are only two terms, "$x^{5}$" and "3". The $x^{5}$ term has a degree of 5, its exponent. The 3 term has a degree of zero, because you could write it as $3 * x^{0} = 3 * 1$ using the zero exponent rule.

The degrees present are 5 and 0. Choose the highest one, 5. So, the answer here is D.