Polynomial Brain-Twisters

Date: 12/4/95 at 14:58:46
From: "Jonathan Howard"
Subject: Polynomial Brain-Twisters

Hello, I'm stumped on some similar polynomial problems.  I heard 
you were the best in the land, so here they are:

1) If m, n, and 1 are non-zero roots of the equation x^3-mx^2+nx-1=0 
   then what is the sum of the roots?

2) Solve 2x^3-3x^2+1=0.

These are the type of problems that don't take long to solve, however 
I keep getting caught up on them.  I was working on them using the 
remainder, integral root, and factor theorems.

Any help would be greatly appreciated.

Yours,
J. Howard

Date: 8/16/96 at 17:33:0
From: Doctor James
Subject: Re: Polynomial Brain-Twisters

I can give you some hints:

1)  If 1 is a root of the equation, it means that you can divide
the equation by (x-1) and the remainder has to be zero. If you do 
that, you should get a nice expression involving n and m.

2)  Try several roots of {+-1, +-2, +-3, +-1/2, +-3/2, +-1/3, +-2/3}
by dividing the expression by (x-<root>). If you don't get a 
remainder, you know that root is right! Once you do that, you should 
have a quadratic equation that should't be too hard to solve.

If you need more help with those, please write back!

-Doctor James,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/