00:01
How many roots does the function have? and the function is x cubed minus 3x plus 1, that entire term squared.
00:08
Well, roots are just essentially your x and y values or the answers to the problem.
00:16
Here, they're going to be your x values.
00:20
And in this case, you're going to have six roots.
00:24
Let me show you what why and how i got this number.
00:27
So you're going to have x3 minus 3x plus 1.
00:30
Because of the parentheses, what we're going to have to do is we're going to square that entire value.
00:36
So that means we're going to multiply it by itself.
00:38
So we're going to have x3 minus 3x plus 1, all of that times x cubed minus 3x plus 1.
00:46
So now we can do some basic distribution, x to the cubed and x cubed, when you multiply those together, you're going to end up with x to the sixth, then you're going to have minus 3x, or plus x cubed.
01:02
So what i did was i just took this first x cubed, and i multiplied it by each one of the terms in the second set of the parentheses.
01:11
So now i'm going to do the same thing with the minus 3x.
01:16
So what that's going to be is it's going to be minus 3x to the fourth plus 9x squared minus 3x.
01:27
And then finally, what we're going to do is we're going to do the one...