Question

how many roots, real and imaginary, does the following polynomial have?
$f(x)=x^{4}-8x^{3}+15x^{2}+7x - 3$
1
2
3
4
remember, the total number of roots is equal to the degree of the polynomial. the degree is the largest exponent on a variable.

Explanation:

Step1: Identify polynomial degree

The polynomial is $f(x)=x^{4}-8x^{3}+15x^{2}+7x - 3$. The highest - power of $x$ is 4, so the degree $n = 4$.

Step2: Apply fundamental theorem of algebra

According to the fundamental theorem of algebra, the number of roots (counting multiplicities) of a polynomial of degree $n$ is equal to $n$. So the number of real and imaginary roots of $f(x)$ is 4.

Answer:

4