NCSSM Placement Practice Test

Question: 1 / 570

What value does a discriminant of zero indicate?

Two real roots

No real roots

One real root

A discriminant of zero indicates that a quadratic equation has exactly one real root, also known as a double root. This situation arises because when the discriminant, which is calculated as \( b^2 - 4ac \), equals zero, it means the quadratic formula results in one unique solution rather than two distinct solutions.

To elaborate, the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) relies on the discriminant for determining the nature of the roots. When the discriminant is zero, the square root term becomes zero, simplifying the formula to \( x = \frac{-b}{2a} \). This shows that the graph of the quadratic function touches the x-axis at a single point, leading to the conclusion that there is only one real root.

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Two imaginary roots

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