Accuplacer Advanced Algebra and Functions Practice Exam 2025 – Complete Preparation

Question: 1 / 400

What does a negative discriminant indicate about the solutions of a quadratic equation?

No real solutions

Two real solutions

One real solution

Two imaginary solutions

A negative discriminant in the context of a quadratic equation indicates that the solutions to the equation are not real numbers. Specifically, when the discriminant (the expression under the square root in the quadratic formula, given by \( b^2 - 4ac \)) is negative, the square root of a negative number leads to complex solutions.

The quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), results in two complex solutions when the discriminant is negative. This means that both roots involve an imaginary component, reflecting the fact that you cannot take the square root of a negative number within the realm of real numbers. Thus, these solutions are described as two imaginary solutions.

Understanding that a negative discriminant leads to imaginary solutions is crucial for recognizing the nature of the roots of quadratic equations and where they lie on the complex plane.

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