Question

According to the fundamental theorem of algebra, how many zeros does thepolynomial below have?f(x) = x² + 5x³ + 10x² + 20x+24Answer here

Answer 1

Given:

`f(x)=x^2+5x^3+10x^2+20x+24`

Required:

We need to find the number of zeros of the given polynomial.

Step-by-step explanation:

Recall that the Fundamental Theorem of Algebra states that for any polynomial of degree n, there are n zeros, some of which may be complex.

The highest exponent of the given polynomial is 3.

We know that the degree of the polynomial is the highest exponent.

The degree of the given polynomial is 3.

By the Fundamental Theorem of Algebra, there are 3 zeros.

Final answer:

The given polynomial has 3 zeros.