Chapter 9: Q.9 (page 869)

Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $\frac{4}{3} x^{2} = 48$

Short Answer

Expert verified

The solution of the quadratic equation: $x = 6, x = - 6$

Step by step solution

Step 1. Given information

Consider the quadratic equation $\frac{4}{3} x^{2} = 48$

The objective is to solve the quadratic equation by using the square root property.

If $x^{2} = k$ , then $x = \pm \sqrt{k}$

The quadratic term is isolated. Divide by $\frac{3}{4}$ to make its coefficient 1.

$\frac{3}{4} (\frac{4}{3} x^{2}) = \frac{3}{4} (48) x^{2} = 36$

Step 2. Apply square root property

So, $x = \pm \sqrt{36}$

Simplify the radical.

role="math" localid="1645636382479" $x = \pm \sqrt{6 \cdot 6} x = \pm 6$

Rewrite to show two solutions.

$x = 6, x = - 6$

Step 3. Check the solutions

Substitute $x = 6$ in the original equation.

role="math" localid="1645636601121" $\frac{4}{3} x^{2} = 48 \frac{4}{3} {(6)}^{2} \overset{?}{=} 48 4 (12) \overset{?}{=} 48 48 = 48$

Substitute $x = - 6$ in the original equation.

$\frac{4}{3} x^{2} = 48 \frac{4}{3} {(- 6)}^{2} \overset{?}{=} 48 4 (12) \overset{?}{=} 48 48 = 48$

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Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $\frac{4}{3} x^{2} = 48$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Apply square root property

Step 3. Check the solutions

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Solve Quadratic Equations of the Form ax2=kUsing the Square Root Property.In the following exercises, solve each equation43x2=48

Short Answer

Step by step solution

Step 1. Given information

Step 2. Apply square root property

Step 3. Check the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Pure Maths

Geometry

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $\frac{4}{3} x^{2} = 48$