# Explain how to determine if an equation has one solution.

## Question:

Explain how to determine if an equation has one solution.

## Roots of an Equation

If a value is defined to be the root of an equation, it means that it is a solution to that equation. This value satisfies the equation and maybe graphically represented as the point where the equation touches the x-axis.

## Answer and Explanation:

The number of maximum solutions relies on the degree of the independent variable considered equation. Thus for a quadratic equation, the degree, or exponent, is 2, and therefore, there are at most 2 solutions. For a cubic equation, of the third degree, the maximum number of solutions is 3. So, An equation has one solution if the **independent variable is of the first degree**, which is the case for a linear equation.

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from HSC Mathematics: Exam Prep & Syllabus

Chapter 20 / Lesson 3