00:01
Given r sub 1 equals 6 minus 5i and r sub 2 equals 6 plus 5i, these are the given roots of a quadratic equation.
00:09
And we're going to find that quadratic equation to put it in standard form of ax squared plus bx plus c equals 0.
00:16
Let's take a look.
00:18
These are my factors.
00:19
We can work backwards.
00:21
Technically, if we can put an x here, so we get x sub 1.
00:25
I'm just actually going to leave that as x.
00:27
X equals 6 minus 5i.
00:30
And i want to be able to set x equal to zero.
00:32
So i'm going to subtract 6 and add 5i to both sides so that i get zero on that side.
00:39
And i get x minus 6 plus 5i equals 0.
00:42
And we do the same thing here.
00:44
X equals 6 plus 5i.
00:46
Subtract 6, subtract 6 or 5i from both sides.
00:54
So we get 0 over there.
00:55
And i get x minus 6 minus 5i equals 0.
00:59
These are my factors.
01:02
And now we can put this together and i get x minus six plus five i times x minus six minus five i...