1310-Notes-Sec-43-filled

1310-Notes-Sec-43-filled - Math 1310 Section 4.3 Roots of...

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Math 1310 Section 4.3 Roots of Polynomials Finding real and complex roots (zeros) of a polynomial You’ll need to be able to find all of the zeros of a polynomial. You’ll now be expected to find both real and complex zeros of a function. A polynomial of degree 1 n has exactly n zeros, counting all multiplicities. To find all zeros, you’ll factor completely. From the factored form of your polynomial, you’ll be able to read off all the zeros of the function. If c is a zero of a polynomial P , then c x = is a root of the equation 0 ) ( = x P . If your polynomial has real coefficients, then the polynomial may have complex roots. Complex roots occur in pairs, called complex conjugate pairs. This means that if bi a + is a root of P then so is bi a - . Example 1: Find all zeros of the polynomial, and state the multiplicity of each. Then write the polynomial in completely factored form. 25 10 ) ( 2 + - = x x x P Example 2: Find all zeros of the polynomial, and state the multiplicity of each. Then write the polynomial in completely factored form. 81 ) ( 2 - = x x P
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This note was uploaded on 02/22/2012 for the course MATH 1310 taught by Professor Marks during the Summer '08 term at University of Houston.

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1310-Notes-Sec-43-filled - Math 1310 Section 4.3 Roots of...

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