Analyze the zeros of f(x)=x^4-3x^3-2x^2+3x-5

determine the number of complex zeros.

a.2

c.1

b.4

d.3

a. 2

Step-by-step explanation:

The given function is

.

We can see from the graph that the graph has two x-intercepts.

This means that the function has two real zeros.

By the fundamental theorem of Algebra, the function is supposed have four roots since it is a polynomial of degree 4.

Therefore, the other two zeros are complex.

See graph

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form