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Chapter 4: Q. 12 (page 215)

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

The degree is 5 and zeros are0,1,2,i

Short Answer

Expert verified

The remaining zero of the polynomial is -i.

Step by step solution

01

Step 1. Given Information

The polynomial has degree 5 and four zeros are0,1,2,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 a-ibas another zero.

03

Step 3. Explanation

Since the function has coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that -i, the conjugate of i is the remaining zero.

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