Consider the equation x3 x2 x 1 0. (a) Use Descartess rule to show that the equation has
Chapter 12, Problem 55(choose chapter or problem)
Consider the equation x3 x2 x 1 0. (a) Use Descartess rule to show that the equation has either one or three negative roots. (b) Now show that the equation cannot have three negative roots. Hint: Multiply both sides of the equation by x 1. Then simplify the lefthand side and reapply Descartess rule to the new equation. (c) Actually, the original equation can be solved using the basic factoring techniques discussed in Appendix B.4. Solve the equation in this manner. 15
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