00:01
In the polynomial equation 4x cubed minus 12x squared minus 9x minus 1 equals 0, we want to find the solutions using the rational zero theorem and descartes rule of signs.
00:21
So the rational zero theorem says all the possible rational zeros are formed by the factors of the leading coefficient.
00:33
Which is, or excuse me, the constant, which is just one, over the factors of the leading coefficient, which is positive negative 1, 2, and 4 going to 4, which means the possibilities are positive or negative 1, 1 half, or 1 4th.
00:55
So let's see if 1 is a 0.
01:00
We can synthetically divide 1 from the coefficients and see what kind of remainder we get a remainder of 0, then it is in 6.
01:10
So we drop down the 4, multiply, add, multiply, add, multiply, add, not a solution.
01:19
We can try negative 1.
01:25
Drop down the 4, multiply, add, then multiply and add, also not a solution.
01:47
Let's try 1 half...