Question

1. $f(x)=x^6 - 5x^4 - x^2 + 5$

a) 8
b) 6
c) 4
d) 5
use the fundamental theorem of algebra to state the number of zeros/solutions/roots of the polynomial.

Explanation:

Step1: Recall Fundamental Theorem of Algebra

A polynomial of degree $n$ has exactly $n$ complex zeros (counting multiplicities).

Step2: Identify polynomial degree

For $f(x)=x^6 - 5x^4 - x^2 + 5$, the highest power of $x$ is $6$, so degree $n=6$.

Step3: Apply theorem to find zeros

By the theorem, the number of zeros equals the degree.
$n=6$

Answer:

B) 6