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Chapter 4: Q. 9 (page 215)

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

The degree is 4 and zeros are role="math" localid="1646221442495" i,1+i

Short Answer

Expert verified

The two remaining zeros of the polynomial are-i,1-i.

Step by step solution

01

Step 1. Given Information

The polynomial has degree 4 and two zeros areiand1+i.

02

Step 2. Concept

Conjugate Pair Theorem says that if a polynomial with degree n with real coefficient, has one complex zero of the form a+ib then the polynomial should have the conjugate pair of a+ib that is a-ib as another zero.

03

Step 3. Explanation

Since fxhas coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that -i, the conjugate of i, and 1-i, the conjugate of 1+i, are the two remaining zeros.

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