Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What type of equation is represented by the form ax² + bx + c = 0?

1. Linear equation

2. Quadratic equation

3. Cubic equation

4. Polynomial expression

The correct answer is: Quadratic equation

The form ax² + bx + c = 0 represents a quadratic equation. In this equation, 'a', 'b', and 'c' are coefficients where 'a' cannot be zero, as this would change the nature of the equation. The defining characteristic of a quadratic equation is the presence of the x² term, which indicates that the highest exponent of the variable x is 2. This unique aspect leads to the formation of a parabolic graph when plotted, showcasing its distinct properties and behaviors compared to linear, cubic, or more complex polynomial expressions. Quadratic equations can have two real solutions, one real solution, or no real solutions at all, depending on the discriminant (b² - 4ac). Thus, the correct identification of the equation type is fundamental in understanding the underlying mathematics and the behavior of parabolic functions.