Chapter 9.6, Problem 3P

(a)

To determine

Find the method you would use to solve the equation.

Answer to Problem 3P

Factoring

Explanation of Solution

Given :

  $x^2-8x+12=0$ .

Calculation:

Given :

  $x^2-8x+12=0$

Comparing the equation with standard quadratic equation, a = 1 , b = -8, c = 12

So, the discriminant is :

  $\begin{array}{l}{b}^2-4ac\\ ={(-8)}^2-4(1)(12)\\ =64-48\\ =16\end{array}$

which is a perfect square.

So, the equation can be solved by factoring the middle term.

(b)

To determine

Find the method you would use to solve the equation.

Answer to Problem 3P

Completing the square.

Explanation of Solution

Given :

  $169x^2=36$ .

Calculation:

Given :

  $169x^2=36$

Since both the numbers are perfect square , so ,

  $\begin{array}{l}{x}^2=\frac{36}{169}\mathrm{........}[\text{divide each side by 169]}\\ \Rightarrow x=\pm \frac{6}{13}\mathrm{......}[\text{take square root each side]}\end{array}$

So, the equation can be solved by completing the square.

(c)

To determine

Find the method you would use to solve the equation.

Answer to Problem 3P

Quadratic formula

Explanation of Solution

Given :

  $5x^2+13x-1=0$ .

Calculation:

Given :

  $5x^2+13x-1=0$

Comparing the equation with standard quadratic equation, a = 5 , b = 13, c = -1

So, the discriminant is :

  $\begin{array}{l}{b}^2-4ac\\ ={(13)}^2-4(5)(-1)\\ =169+20\\ =189\end{array}$

which is not a perfect square.

So, the equation can be solved by quadratic formula.