AFOQT Practice Test

If the discriminant is negative, what can be concluded about the roots of the equation?

1. There are two real roots

2. There is one real root

3. There are no real roots

4. There are three real roots

The correct answer is: There are no real roots

When the discriminant of a quadratic equation is negative, it indicates that the equation does not intersect the x-axis at any point. In terms of the roots, this means that the roots are not real numbers; rather, they are complex conjugates. In the context of a quadratic equation of the form \( ax^2 + bx + c = 0 \), the discriminant is calculated as \( b^2 - 4ac \). A negative value for this expression signifies that there is no solution in the realm of real numbers, confirming that the equation has no real roots. Thus, the conclusion that there are no real roots is indeed the correct assessment given a negative discriminant.