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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.6 (page 863)

Solve $q^{2} + 24 = 0$

Short Answer

Expert verified

The solutions of the quadratic equation: $q = 2 \sqrt{6} i, q = - 2 \sqrt{6} i$

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

$q^{2} + 24 = 0$

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

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

Isolate the quadratic term.

$q^{2} = - 24$

Use the Square Root Property.

localid="1645358604148" $q = 卤 \sqrt{- 24}$

02

Step 2. Simplify the expression.

Simplify using complex numbers.

$q = 卤 \sqrt{24} i$

Simplify the radical.

$q = 卤 2 \sqrt{6} i$

Rewrite to show two solutions.

$q = 2 \sqrt{6} i, q = - 2 \sqrt{6} i$

03

Step 3. Check the solutions:

Substitute $q = 2 \sqrt{6} i$ in the original equation.

$q^{2} + 24 = 0 {(2 \sqrt{6} i)}^{2} + 24 \overset{?}{=} 0 4 (6) i^{2} + 24 \overset{?}{=} 0 24 (- 1) + 24 \overset{?}{=} 0 0 = 0$

Substitute $q = - 2 \sqrt{6} i$ in the original equation.

$q^{2} + 24 = 0 {(- 2 \sqrt{6} i)}^{2} + 24 \overset{?}{=} 0 4 (6) i^{2} + 24 \overset{?}{=} 0 24 (- 1) + 24 \overset{?}{=} 0 0 = 0$

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Most popular questions from this chapter

In the following exercises, solve by using the Quadratic Formula.
$25 d^{2} - 60 d + 36 = 0$

In the following exercises, solve by using the Quadratic Formula.

$8 x^{2} - 4 x + 1 = 0$

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation.

In the following exercises, determine the number of solutions for each quadratic equation.

(a) $4 x^{2} - 5 x + 16 = 0$

(b) localid="1645008653364" $36 y^{2} + 36 y + 9 = 0$

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Solve by using the Quadratic Formula: $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$

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