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Chapter 1: Problem 118

Explain how to recognize an equation that is quadratic in form. Provide two original examples with your explanation.

Short Answer

Expert verified
Essentially, an equation is quadratic if it can be arranged in the form ax^2 + bx + c = 0, with the highest power of the variable being 2 and 'a' not equating to 0. An example could be 5x^2 + 3x - 8 = 0 or -2x^2 - 7x + 3 = 0.

Step by step solution

01

Understand the structure of a quadratic equation

A quadratic equation, in standard form, is written as ax^2 + bx + c = 0. The power of x stands at 2, making it a second degree polynomial. 'a' should not be equal to 0, where 'a', 'b' and 'c' are constants.
02

Identify the quadratic form in an equation

Upon examining an equation, if you find a variable that is squared, or if the equation can be rearranged into the form ax^2 + bx + c = 0, then the equation is quadratic in form.
03

Example 1 of a quadratic equation

Consider the equation 5x^2 + 3x - 8 = 0. This equation aligns with the aforementioned standard form for it has 'x' raised to the power of 2 which denotes it as being a quadratic equation.
04

Example 2 of a quadratic equation

Consider the equation -2x^2 - 7x + 3 = 0. Similar to Step 3, this equation matches the standard form, constituting it as a quadratic equation as it has 'x' to the power of 2.

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