00:01
So we want to find a polynomial, and we want it to be its lowest degree.
00:06
Because if we don't have that characteristic that it's lowest degree, there actually are infinitely many answers.
00:11
So lowest degree.
00:13
And we want it to have rational coefficients.
00:15
That's very, very important.
00:17
That means that if we have a complex zero, they have to come as complex conjugates, and we do have one.
00:23
And we want zeros to take place at negative 4i and at 5.
00:30
Now, because of this complex zero, we know there must be another one.
00:37
They have to come as complex conjugates if we're going to have rational coefficients.
00:41
So we know there's another zero at 4i.
00:45
And remember that a factor, if you know a zero, you know a factor.
00:50
And we take x minus a zero, and that will be a factor.
00:55
So let's write our polynomial.
00:57
Well, we'll do in blue.
00:58
We'll call it f of x...