Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the formula for solving quadratic equations?

1. -b±[√b²-4ac]/2a

2. (y₂-y₁)/(x₂-x₁)

3. y=mx+b

4. (a-b)(a+b)

The correct answer is: -b±[√b²-4ac]/2a

The formula for solving quadratic equations is derived from the standard form of a quadratic equation, which is ax² + bx + c = 0. To find the solutions (or roots) of the equation, we can use the quadratic formula, which is given by -b ± √(b² - 4ac) / (2a). This formula is essential because it provides a systematic way to calculate the values of x that satisfy the quadratic equation, regardless of the specific values of a, b, and c, as long as a is not equal to zero (since that would not represent a quadratic equation). The term √(b² - 4ac) is known as the discriminant, and it indicates the nature of the roots. If the discriminant is positive, there are two distinct real roots; if it is zero, there is exactly one real root; and if it is negative, the roots are complex or imaginary. The other options presented are used in different contexts. The formula for (y₂ - y₁)/(x₂ - x₁) relates to the slope of a line in coordinate geometry. The equation y = mx + b describes the slope-intercept form of a linear equation, which