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Chapter 4: Q. 13 (page 215)

Find the remaining zeros offx with real coefficients and given information.

The degree is 4 and zeros arei,2,-2

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 4 and three zeros arei,2,-2.

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 isa-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 ofi is the remaining zero.

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Most popular questions from this chapter

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)=-4x3-x2+x+2

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

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

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

x3+8x2+11x-20

Make up a polynomial function that has the following characteristics: crosses the x-axis at -1and 4, touches the x-axis at 0and 2, and is above the x-axis between 0and2. Give your polynomial function to a fellow classmate and ask for a written critique

Analyze each polynomial function using Steps 1through 8:

f(x)=x4+x3-3x2-x+2.
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