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Chapter 4: Q. 16 (page 215)

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

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

Short Answer

Expert verified

The remaining three zeros of the polynomial are-i,3+2i,-2-i.

Step by step solution

01

Step 1. Given Information

The polynomial has degree 6 and three zeros arei,3-2i,-2+i.

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-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 of i, 3+2i, the conjugate of 3-2i, and -2-i, the conjugate of -2+i are the remaining three zeros.

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Most popular questions from this chapter

In Problems 49鈥� 60, for each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|

f(x)=3(x-7)(x+3)2

Find a rational function that might have the given graph.

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

f(x)=3x3-7x2+12x-28

x3+2x2-3x>0

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000cubic inches. See the illustration.

Part (a): Express the surface area S of the box as a function of x.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?
See all solutions

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