Chapter 15, Problem 108E

Solve each of the expressions for x using the quadratic formula and the x is small approximation. In which of the following expressions is the x is small approximation valid?

a. ${\text{x}}^{\text{2}}/\left(0.\text{2}-\text{x}\right)=\text{1}.\text{3}\times \text{1}{0}^{\text{4}}$
b. ${\text{x}}^{\text{2}}/\left(0.\text{2}-\text{x}\right)=\text{1}.\text{3}$
c. ${\text{x}}^{\text{2}}/\left(0.\text{2}-\text{x}\right)=\text{1}.\text{3}\times \text{1}{0}^{\text{-4}}$
d. ${\text{x}}^{\text{2}}/\left(0.01-\text{x}\right)=\text{1}.\text{3}\times \text{1}{0}^{\text{-4}}$

In a complete sentence, describe the factor(s) that tend to make the x is small approximation valid in an expression.