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Conjugate Pairs Theorem - P((x)-0 is a polynomial equation with real coefficients and the complex number a+bi (b#0) is a root, then a-bi is also a root. Create a polynomial equation with real coefficients that has 2 and 1-i as roots.

Conjugate Pairs Theorem - P((x)-0 is a polynomial equation with real coefficients and the complex number a+bi (b#0) is a root, then a-bi is also a root. Create a polynomial equation with real coefficients that has 2 and 1-i as roots.

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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Conjugate Pairs Theorem - P(x)=0 is a polynomial equation with real coefficients and the complex number a+bi (b#0) is a root, then a-bi is also a root. Create a polynomial equation with real coefficients that has 2 and 1-i as roots. Descartes's Rule of Signs - Suppose P(x)=0 is a polynomial equation with real coefficients and with terms written in descending order. The number of positive real roots of the equation is either equal to the number of variations of sign of P(x) or less than that by an even number. The number of negative real roots of the equation is either equal to the number of variations of sign of P(-x) or less than that by an even number Discuss the possibilities for the roots to : 2x -5x² -6x+4=0 3x - 5x –x -8x+4=0
Transcribed Image Text:Conjugate Pairs Theorem - P(x)=0 is a polynomial equation with real coefficients and the complex number a+bi (b#0) is a root, then a-bi is also a root. Create a polynomial equation with real coefficients that has 2 and 1-i as roots. Descartes's Rule of Signs - Suppose P(x)=0 is a polynomial equation with real coefficients and with terms written in descending order. The number of positive real roots of the equation is either equal to the number of variations of sign of P(x) or less than that by an even number. The number of negative real roots of the equation is either equal to the number of variations of sign of P(-x) or less than that by an even number Discuss the possibilities for the roots to : 2x -5x² -6x+4=0 3x - 5x –x -8x+4=0
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