Chapter 8.7, Problem 25WE

To determine

To solve: the equation.

Answer to Problem 25WE

The equation have no rational roots.

Explanation of Solution

Given information:

The equation is $0.2x^3-0.5x^2+0.8x-2.0=0$ .

Calculation: by using rational root theorem,

The ratio of constant term and coefficient of highest degree term is $\frac{2.0}{0.2}=10$ .

Thus, the total possible rational roots are $\pm 1,\pm 2,\pm 5\text{ and }\pm 10$ .

Now use the synthetic division,

$1$	$0.2$	$-0.5$	$0.8$	$-2.0$
		$0.2$	$-0.3$	$0.5$
	$0.2$	$-0.3$	$0.5$	$-1.5$

$-1$	$0.2$	$-0.5$	$0.8$	$-2.0$
		$-0.2$	$0.7$	$-1.5$
	$0.2$	$-0.7$	$1.5$	$-3.5$

$-2$	$0.2$	$-0.5$	$0.8$	$-2.0$
		$-0.4$	$1.8$	$-5.6$
	$0.2$	$-0.9$	$2.6$	$-7.6$

$2$	$0.2$	$-0.5$	$0.8$	$-2.0$
		$0.4$	$-0.2$	$1.2$
	$0.2$	$-0.1$	$0.6$	$-0.8$

None of these rational roots satisfy the equation.

Thus, the equation have no rational roots.