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# Class Note for MATH 1310 at UH

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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
Math 13 10 Chapter 4 Section 43 Roots of Polynomials Zeros of Polynomials If c is a zero of the polynomial Px then x c is a root of the equation Px 0 Recall The Factor Theorem 0 is a zero of Px if and only ifx i c is a factor of Px If a factor x i 0 appears k times in the complete factorization of Px then we say that c is a zero of multiplicity k A polynomial of degree n 3 1 has exactly 11 zeros counting multiplicities Complex Zeros For a polynomial with real coefficients complex zeros occur in complex conjugate pairs that is if the complex number a bi is a zero of Px then its complex conjugate a i bi is also a zero of Px Now a2 12 abia bi Example 1 Factor the following polynomial find its zeros and state the multiplicity of each zero Px x2 6x9 Example 2 Factor the following polynomial find its zeros and state the multiplicity of each zero Px x2 121 Example 3 Factor the following polynomial find its zeros and state the multiplicity of each zero Px x6 4x4 Example 4 Factor the following polynomial find its zeros and state the multiplicity of each zero Px x3 3x2 25x 75 Example 5 Find a polynomial with integer coefficients that satisfies the given conditions Degree of the polynomial 2 Zeros 2 7 Example 6 Find a polynomial with integer coefficients that satisfies the given conditions Degree of the polynomial 3 Zeros z39 3 Example 7 Find a polynomial with integer coefficients that satisfies the given conditions Degree of the polynomial 3 Zeros l 5139 Constant Coefficient 50

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