00:01
In this question, we are going to find the remaining zeros of the given quartic function, given one complex zero.
00:13
If we know x is negative 2i, complex zeros come in conjugate pairs, which means we also have x equals 2i.
00:27
Let's write those as factors.
00:35
And now let's multiply them together.
00:37
X squared minus 2x i plus 2x i minus 4 i squared i squared is negative 1 so we end up with x squared plus 4 that is a factor of the quartic function so we will use long division to find the remaining factor 4x to the 4th divided by x squared is 4x squared distribute distribute while you distribute line up like terms.
01:42
Next we need to subtract.
01:46
We will get 15x cubed.
01:50
12 minus 16 is a negative 4.
01:53
That was an x cubed.
01:55
I said it right, but didn't write it.
01:59
Minus 4x squared.
02:02
And we will bring down.
02:06
15x cubed divided by x squared is 15x.
02:15
Distribute.
02:21
Line up like terms, subtract, leaving negative 4x squared plus zero, and we bring down the minus 16.
02:42
Last division step.
02:45
Negative 4x squared divided by x squared is negative 4...