finding roots of cubic functions

• Apr 6th 2009, 08:38 PM
amyu2005
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)
• Apr 6th 2009, 08:44 PM
Jhevon
Quote:

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
• Apr 6th 2009, 08:46 PM
TheEmptySet
Quote:

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 $\pm 1$ but neither of these are zero's.

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

Is there a typo?