Chapter 9.4, Problem 3E

To determine

To explain is it more convenient to complete the square for $x^2+bx$ when b is odd or when b is even.

Answer to Problem 3E

When b is odd then less convenient to calculate the ${\left(\frac{b}{2}\right)}^2$ and needs extra steps

When b is even then more convenient to calculate the ${\left(\frac{b}{2}\right)}^2$ and needs less extra steps

Explanation of Solution

Given information:

To complete the square for $x^2+bx$ when b is odd or when b is even.

Calculation:

To complete the square for $x^2+bx$ when b is odd or when b is even.

Put $x^2+bx=0$

Since ${\left(\frac{b}{2}\right)}^2=\frac{b^2}{4}$ , add $\frac{b^2}{4}$ to both sides

When b is odd then less convenient to calculate the ${\left(\frac{b}{2}\right)}^2$ and needs extra steps

When b is even then more convenient to calculate the ${\left(\frac{b}{2}\right)}^2$ and needs less extra steps