00:01
Okay, so if we have a polynomial and we want to find all of its zeros and then factor it completely, so let's say cubex is equal to x squared plus 2x plus 2.
00:22
Okay, so we cannot factor this without using the quadratic formula.
00:29
So that's exactly what we're going to do.
00:31
So our first step to finding the zeros is to factor.
00:34
And so what we're going to do is we're going to use the quadratic formula.
00:37
Formula x equals negative b in this case it's two plus or minus square root b squared so two squared minus four a which in this case it's one and c which is two the constant this is all under the root and this is all over 2a and it's one so it's just two okay so now let's try to combine some things under the root.
01:15
When we do that, we have so two squared is four, and four times two times one is eight.
01:21
So four minus eight is negative four.
01:24
So we have x equals negative two plus or minus the square root of negative four over two.
01:35
Okay, we can reduce this again because the square root of four is two, and we know the square root of negative one is i.
01:43
So it's going to become negative two plus or minus to i over two.
01:51
And now look, we can reduce again because this all has a factor of two.
01:55
So this is going to equal negative one plus or minus i...