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Chapter 1: Q.14 (page 28)

In Problems 5–16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between - 10 and 10. $\frac{1}{4} x^{3} - 5 x = \frac{1}{5} x^{2} - 4$

Short Answer

Expert verified

The approximate values of X are $x = 0.8, x = - 4.47213 \dots, x = 4.47213 \dots$

Step by step solution

01

Step 1. Given equation and simplification

$\frac{1}{4} x^{3} - 5 x = \frac{1}{5} x^{2} - 4 \Rightarrow 5 x^{3} - 100 x = 4 x^{2} - 80 \Rightarrow 5 x^{3} - 4 x^{2} - 100 x + 80 = 0$

02

Step 2.Graph and x-intercepts

X-intercepts are $x = \frac{4}{5}, x = - 2 \sqrt{5}, x = 2 \sqrt{5}$

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Most popular questions from this chapter

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (3, 4)

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

$(4, 2); (- 5, 2)$

Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

Can the equation of every line be written in slope–intercept form? Why?

For the line $2 x + 3 y = 6$ , the $x -$ intercept is _____ and the $y -$ intercept is _______.

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