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Chapter 4: Q. 7 (page 215)

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

The degree is 3 and zeros are 3.4-i

Short Answer

Expert verified

The remaining zero of the polynomial is4+i.

Step by step solution

01

Step 1. Given Information

The polynomial has degree 3 and two zeros are 3and4-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+bi then the polynomial should have the conjugate pair of a+ib that is a-ib as another zero.

03

Step 3. Explanation

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

It follows that 4+i, the conjugate of 4-i, is the remaining zero.

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