I am reading a book called College Algebra and it defines polynomials as an expression of the form $a_nx^n + a_{n-1}x^{n-1} + ...+ a_2x^2 + a_1x + a_0$ where $a_j$ are real numbers ( I'll stop the definition there). Does polynomials only have real coefficients or it can be complex numbers?
I asked this on a wrong place (Cross Validated) my bad.
Polynomials can also have complex coefficients. There is actually quite a bit of work related to the topic. See, for example, here or here.
An example of such a polynomial would be
$$(42+42i)x^2+(7+i)x.$$
The roots of the above polynomial are at $$x=0 $$ and $$ x = -\frac{2}{21} + \frac{i}{14}.$$
So, nobody hinders you to create polynomials with complex coefficients.
To be clear, it's better to state over which ring the polynomial is defined.
A polynomial in $X$ over a ring $R$ is defined as $\sum\limits_{k = 0}^n = a_kX^K$, where $a_k \in R$ for $k \in \{0,\dots,n\}$.
In particular, a polynomial over $\Bbb{R}$ admits only real coefficients, whereas a polynomial over $\Bbb{C}$ admits complex coefficients.
Remarks: For pedagogical reasons, when one find roots (of polynomials) in algebra-precalculus, one usually focus on real roots and discard the complex ones, especially in exercises of quadratic-equation. I guess it's a possible reason that your College Algebra book only consider polynomials with real coefficients. Things will become clearer when you move on to abstract-algebra.
