Question

determine the number of roots of the function (f(x)=x^{5}-9x^{4}+25x^{3}-15x^{2}-26x + 24).
1
0
5
3

Explanation:

Step1: Recall the fundamental theorem of algebra

The fundamental theorem of algebra states that the number of roots (counting multiplicities) of a non - zero polynomial $P(x)=a_nx^n + a_{n - 1}x^{n - 1}+\cdots+a_1x + a_0$, where $a_n
eq0$ and $n\geq1$, is equal to its degree $n$.

Step2: Identify the degree of the given polynomial

The function $f(x)=x^{5}-9x^{4}+25x^{3}-15x^{2}-26x + 24$ is a polynomial. The highest - power of $x$ in the polynomial is $n = 5$. So, the degree of the polynomial $f(x)$ is $5$.

Answer:

C. 5