Problem 5 Match the equation in Column I w... [FREE SOLUTION]

91影视

Precalculus Student Solutions Manual 5th

Margaret L. Lial, John Hornsby, David I. Schneider

$Math Studyset 91影视 Explanations$ Math

5 Edition

Chapter 1: Problem 5

Match the equation in Column I with its solution $(s)$ in Column II. A. $\pm 5 i$ B. $\pm 2 \sqrt{5}$ C. $\pm i \sqrt{5}$ D. $5$ E. $\pm \sqrt{5} \quad$ F. $-5$ G. $\pm 5$ H. $\pm 2 i \sqrt{5}$ $$x^{2}=-20$$

Short Answer

Expert verified

H. $ \pm 2 i \sqrt{5} $

Step by step solution

- Understand the Given Equation

The equation given is $ x^2 = -20 $. This is a quadratic equation.

- Identify Nature of Roots

Since the right-hand side of the equation is negative ($ -20 $), the solutions will be complex numbers containing \'i\' (imaginary unit).

- Solve for x

To solve for $ x $, take the square root on both sides of the equation: \[ x^2 = -20 \ x = \pm \sqrt{-20} \]

- Simplify the Square Root

Since $ -20 $ can be written as $ -1 \times 20 $, we can separate the square root: \[ \sqrt{-20} = \sqrt{-1 \times 20} = \sqrt{-1} \times \sqrt{20} = i \times \sqrt{20} \]

- Write the Final Solution

Recognize that $ \sqrt{20} $ can be simplified to $ 2 \sqrt{5} $. Thus: \[ x = \pm i \times 2 \sqrt{5} \]

- Match With Column II

The simplified solution matches option H: $ \pm 2 i \sqrt{5} $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Complex Numbers

Complex numbers extend the idea of one-dimensional numbers like integers and real numbers to two dimensions. A complex number is typically written in the form $a + bi$, where:

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91影视

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x^{2}=-20$$

Short Answer

Step by step solution

- Understand the Given Equation

- Identify Nature of Roots

- Solve for x

- Simplify the Square Root

- Write the Final Solution

- Match With Column II

Key Concepts

Complex Numbers

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