Q. 193 Explain how to recognize an equa... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 193 (page 906)

Explain how to recognize an equation in quadratic form.

Short Answer

Expert verified

After substituting a variable for another variable, if an equation can be written in the form $a x^{2} + b x + c = 0, a 鈮� 0$ , then the original equation is in quadratic form.

Step by step solution

Step 1. Definition of Quadratic Equation.

The general form of a quadratic equation is:

$a x^{2} + b x + c = 0$

Where, $a$ is a non zero value.

For example: $2 x^{2} + 3 x + 1 = 0$ .

Step 2. Definition of Quadratic Form.

An equation is in quadratic form, if the substitution gives us an equation of the form $a x^{2} + b x + c = 0, a 鈮� 0$ .

For example: $x^{4} - 4 x^{2} - 5 = 0$ , after substituting $x^{2} = u$ in the equation, the equation can be written as $u^{2} - 4 u - 5 = 0$ .

So, the equation $x^{4} - 4 x^{2} - 5 = 0$ is in quadratic form.

Step 3. Conclusion.

After substituting a variable for another variable, if an equation can be written in the form $a x^{2} + b x + c = 0, a 鈮� 0$ , then the original equation is in quadratic form.

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91影视

Explain how to recognize an equation in quadratic form.

Short Answer

Step by step solution

Step 1. Definition of Quadratic Equation.

Step 2. Definition of Quadratic Form.

Step 3. Conclusion.

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