Question

Fan and medal!!
The graph of a polynomial function of degree 5 has three x-intercepts, all with multiplicity 1. Describe the nature and number of all its zeros.
A) The function has 5 real zeros.
B) The function has 3 real zeros.
C) The function has 3 real and 2 imaginary zeros.
D) The function has 2 real and 3 imaginary zeros.

Answer 1

Can you at least have some attempt and explaination?

Answer 2

This is a fifth order polynomial. You are told that its graph has 3 x-intercepts, and that the "multiplicity" of each is 1. That means the graph actually crosses the x-axis at each of these 3 points. A fifth order poly must have 5 zeros. How do you account for the fact that there are only 3 x-intercepts? Have the other two zeros been lost in the mail? ;)

Answer 3

lol. thanks.

Answer 4

I would say b.

Answer 5

mathmale's comment tells you that it can't be b :P By the Fundemental Theorem of Algebra, every nth degree polynomial has exactly n zeros (another name for "zeros" is roots), assuming we are allowing complex numbers.

Answer 6

So a polynomial of degree 5 must always have 5 zeros. So the question is, how can you tell which ones are real and which ones are imaginary... any idea?

Answer 7

not a single clue.

Answer 8

thanks for the help.

Answer 9

Okay lets see this way.
A polynomial with degree of 5 must have 5 zeroes
There can be only two types of zeroes, real and imaginary
If three are real then the remaining two must be?

Answer 10

Got it?

Answer 11

yea

Answer 12

thanks