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Chapter 4: Q. 11 (page 215)

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

The degree is 5 and zeros are1,i,2i

Short Answer

Expert verified

The two remaining zeros of the polynomial are -i,-2i.

Step by step solution

01

Step 1. Given Information

The polynomial has degree 5 and three zeros are1,i,2i.

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 ofa+ibthat is a-ibas another zero. .

03

Step 3. Explanation

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

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

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Most popular questions from this chapter

One solution of the equation x3-8x2+16x-3=0 is 3.

Find the sum of the remaining solutions.

Find the real zeros of f. Use the real zeros to factor f.

f(x)=x3-8x2+17x-6

In Problems 39鈥�56, find the real zeros of f. Use the real zeros to factor f.

f(x)=4x4+15x2-4

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=2x5-x4-x2+1

Find the domain of the rational function.

Rx=xx4-1
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