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Chapter 4: Q. 103 (page 211)

is $\frac{2}{3}$ a zero of $f (x) = x^{7} + 6 x^{5} - x^{4} + x + 2$ ? Explain.

Short Answer

Expert verified

$\frac{2}{3}$ is not a zero of functionlocalid="1646144029599" $f (x) = x^{7} + 6 x^{5} - x^{4} + x + 2$ becouse $f (\frac{2}{3}) \neq 0$

Step by step solution

01

Step 1. Given data

The given function is

$f (x) = x^{7} + 6 x^{5} - x^{4} + x + 2$

Zero of the function is $\frac{2}{3}$

02

Step 2. Verification

Substitute $\frac{2}{3}$ for x in the function

$f (x) = x^{7} + 6 x^{5} - x^{4} + x + 2 f (\frac{2}{3}) = {(\frac{2}{3})}^{7} + 6 {(\frac{2}{3})}^{5} - {(\frac{2}{3})}^{4} + (\frac{2}{3}) + 2 f (\frac{2}{3}) = 3.31 f (\frac{2}{3}) \neq 0$

$f (\frac{2}{3})$ is not equal to zero so $\frac{2}{3}$ is not a zero of the function

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Most popular questions from this chapter

In Problems 21–32, 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.

$f (x) = 2 x^{5} - x^{4} - x^{2} + 1$

Find a rational function that might have the given graph.

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

$f (x) = x^{3} + 6 x^{2} + 6 x - 4$

Find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f.

$f (x) = 2 x^{3} - x^{2} - 11 x - 6$

United Parcel Service has contracted you to design a closed box with a square base that has a volume of $10, 000$ cubic 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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