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1. Consider the equation 2x³-x²-13x-6=0. a. Use Descartes rule of signs to determine the number of possible positive and the number of possible negative roots. b. Use Descartes Rational Root Theorem to see what the possible rational roots are. c. Verify that x = 3 is a root. d. Use long division to reduce the equation to a quadratic equation. e. Solve the resulting quadratic equation to find the remaining root.

1. Consider the equation 2x³-x²-13x-6=0. a. Use Descartes rule of signs to determine the number of possible positive and the number of possible negative roots. b. Use Descartes Rational Root Theorem to see what the possible rational roots are. c. Verify that x = 3 is a root. d. Use long division to reduce the equation to a quadratic equation. e. Solve the resulting quadratic equation to find the remaining root.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the equation 2x³-x²-13x-6=0. a. Use Descartes rule of signs to determine the number of possible positive and the number of possible negative roots. b. Use Descartes Rational Root Theorem to see what the possible rational roots are. c. Verify that x = 3 is a root. d. Use long division to reduce the equation to a quadratic equation. e. Solve the resulting quadratic equation to find the remaining root.
Transcribed Image Text:1. Consider the equation 2x³-x²-13x-6=0. a. Use Descartes rule of signs to determine the number of possible positive and the number of possible negative roots. b. Use Descartes Rational Root Theorem to see what the possible rational roots are. c. Verify that x = 3 is a root. d. Use long division to reduce the equation to a quadratic equation. e. Solve the resulting quadratic equation to find the remaining root.
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