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Chapter 1: Q.11 (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. $- x^{3} - \frac{5}{3} x^{2} + \frac{7}{2} x + 2 = 0$

Short Answer

Expert verified

The values of X are approximately $x \approx - 0.49056 \dots, x \approx 1.51498 \dots, x \approx - 2.69108 \dots$

Step by step solution

01

Step 1. Given equation and simplification

$- x^{3} - \frac{5}{3} x^{2} + \frac{7}{2} x + 2 = 0 \Rightarrow - 6 x^{3} - 10 x^{2} + 21 x + 12 = 0$

02

Step 2.Graph and X-intersection

X-intercepts are $x \approx - 0.49056 \dots, x \approx 1.51498 \dots, x \approx - 2.69108 \dots$

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Most popular questions from this chapter

Find the midpoint of the line segment joining the points P₁ and P₂ .

$P_{1} = (a, a); P_{2} = (0, 0)$

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$x^{3} + x^{2} - 4 x - 4 = 0$

Which of the following equations might have the graph shown? (More than one answer is possible.)

$(a) 2 x + 3 y = 6 (b) - 2 x + 3 y = 6 (c) 3 x - 4 y = - 12 (d) x - y = 1 (e) x - y = - 1 (f) y = 3 x - 5 (g) y = 2 x + 3 (h) y = - 3 x + 3$

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

$(- 2, 3); (2, 1)$

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\frac{4}{y} - 5 = \frac{18}{2 y}$

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