Polynomial Brain-TwistersDate: 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/ |
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