Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the discriminant in the context of a quadratic formula?

1. The portion under the radical of the formula

2. The leading coefficient of the equation

3. The complete quadratic expression

4. The value of the roots

The correct answer is: The portion under the radical of the formula

The discriminant is found within the quadratic formula, which is given by the expression \( ax^2 + bx + c = 0 \). In this context, the discriminant specifically refers to the portion under the square root in the quadratic formula: \( b^2 - 4ac \). This value is crucial because it determines the nature of the roots of the quadratic equation. If the discriminant is positive, there are two distinct real roots; if it is zero, there is exactly one real root (a repeated root); and if it is negative, there are no real roots, but two complex roots. Understanding the discriminant not only helps in identifying the nature of the solutions to the quadratic equation but also plays a significant role in graphing the parabola represented by the quadratic function, as it relates directly to the x-intercepts. Hence, recognizing it as the part under the radical gives clarity to its fundamental role in solving quadratics.