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Chapter 4: Q. 15 (page 215)

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

The degree is 6 and zeros are2,2+i,-3-i,0

Short Answer

Expert verified

The remaining two zeros of the polynomial are2-i,-3+i.

Step by step solution

01

Step 1. Given Information

he polynomial has degree 6 and four zeros are2,2+i,-3-i,0.

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-ib as another zero.

03

Step 3. Explanation

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

It follows that 2-i, the conjugate of 2+i, and -3+i, the conjugate of -3-i, are the remaining two zeros.

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