Question

how many roots, real or complex, does the polynomial $7 + 5x^4 - 3x^2$ have in all?
4
3
7
5

Explanation:

Step1: Identify polynomial degree

The polynomial is $7 + 5x^4 - 3x^2$, which can be rewritten as $5x^4 - 3x^2 + 7$. The highest power of $x$ is 4, so the degree is 4.

Step2: Apply Fundamental Theorem of Algebra

A polynomial of degree $n$ has exactly $n$ roots (real or complex, counting multiplicities). For $n=4$, the number of roots is 4.

Answer:

4