00:01
Given the function, p of x equals x to the fifth minus 9x to the fourth plus 34x cubed minus 50ax squared plus 45x minus 13.
00:15
We want to find all of the zeros.
00:18
Since it's degree 5, there are five of them.
00:20
Let's go to graph and calculator and find the ones that are real.
00:26
And so we have x to the fifth.
00:41
All right, we have minus 13.
01:05
There's the typo.
01:07
All right.
01:08
One is a solution or a zero.
01:12
And there is inflection here, which is a clue that there is some multiplicity here.
01:20
So let's see how much multiplicity we know x is equal to one.
01:24
So let's synthetically divide this out from the coefficients 1, negative 9, 34.
01:29
Negative 58, 45, and negative 13.
01:33
Since there was an inflection and it went through it, i'm thinking multiplicity three.
01:38
Because if it's multiplicity two, remember, it touches and turns around...