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

The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) (where \( n>0 \)) has exactly \( n \) roots (counting multiplicities) in the complex number system.

Step2: Determine the degree of the polynomial

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

Step3: Apply the Fundamental Theorem of Algebra

By the Fundamental Theorem of Algebra, since the degree of the polynomial is 6, the polynomial has 6 zeros (or solutions or roots) in the complex number system.

Answer:

B) 6