# Thread: finding roots of cubic functions

1. ## finding roots of cubic functions

my prof had a cubic function r^3 -4r^2 + 3r -1

& quickly wrote down the roots: (r-1)^2(r-2)

how did he do that so quickly? (he didn't write down the steps)

2. Originally Posted by amyu2005
my prof had a cubic function r^3 -4r^2 + 3r -1

& quickly wrote down the roots: (r-1)^2(r-2)

how did he do that so quickly? (he didn't write down the steps)
um, that's not right. maybe when you get the right function we can show you the trick. there are several tricks that go with cubics. not all are done in the same way

3. Originally Posted by amyu2005
my prof had a cubic function r^3 -4r^2 + 3r -1

& quickly wrote down the roots: (r-1)^2(r-2)

how did he do that so quickly? (he didn't write down the steps)
ummmmm...... I don't think that is correct.

According to the rational roots theorem the only the only zero would be $\displaystyle \pm 1$ but neither of these are zero's.

This does not have any zero's over the rational numbers.

Is there a typo?