Ohio Assessments for Educators (OAE) Mathematics Practice Exam

If the discriminant is zero, how many roots does the quadratic equation have?

1. No roots

2. One root

3. Two distinct real roots

4. One or two complex roots

The correct answer is: One root

When the discriminant of a quadratic equation is zero, it indicates that the equation has exactly one root, which is also known as a repeated or double root. This occurs because the quadratic can be expressed in the form \(ax^2 + bx + c = 0\), and the discriminant is calculated as \(b^2 - 4ac\). When the discriminant equals zero, the quadratic formula simplifies to a single solution: \[ x = \frac{-b}{2a} \] This means there is no variation in values, resulting in the same root counted twice. Thus, a discriminant of zero confirms that there is exactly one real solution for the quadratic equation.