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Chapter 4: Q. 10 (page 215)

Find the remaining zeros of fxwith real coefficients and given information.

The degree is 4 and zeros are1,2,2+i

Short Answer

Expert verified

The remaining zero of the polynomial is2-i.

Step by step solution

01

Step 1. Given Information 

The polynomial has degree 4 and three zeros are 1,2,2+i

02

Step 2. Concept

Conjugate Pair Theorem says that if a polynomial with degree nwith real coefficient, has one complex zero of the form a+ibthen the polynomial should have the conjugate pair of a+ibthat is localid="1646230229883" a-ibas another zero.

03

Step 3. Explanation

Since f has coefficients that are real numbers, complex zeros appear as conjugate pairs. It follows that 2-i, the conjugate of 2+i, is the remaining zero.

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