Chapter 8.7, Problem 24WE

To determine

To solve: the equation.

Answer to Problem 24WE

The equation have no rational roots.

Explanation of Solution

Given information:

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

Calculation: by using rational root theorem,

The ratio of constant term and coefficient of highest degree term is $\frac{0.2}{2.0}=0.1$ .

Thus, the total possible rational roots are $\pm 0.1$ .

Now use the synthetic division,

$0.1$	$2.0$	$-0.8$	$0.5$	$-0.2$
		$.2$	$-0.06$	$.494$
	$2.0$	$-0.6$	$4.94$	$0.294$

$-0.1$	$2.0$	$-0.8$	$0.5$	$-0.2$
		$-0.2$	$0.1$	$-0.06$
	$2.0$	$-1$	$0.6$	$-0.26$

None of these rational roots satisfy the equation.

Thus, the equation have no rational roots.