NBCT Mathematics Adolescence and Young Adulthood (AYA) Component 1 Practice Test

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Which statement correctly describes the case Δ < 0 for a quadratic equation ax^2 + bx + c = 0?

If Δ > 0, there are two real roots.

If Δ = 0, there are two real roots.

If Δ < 0, the roots are complex.

The discriminant of a quadratic, Δ = b^2 - 4ac, tells you the nature of the roots. When Δ is negative, you can’t take the square root of a negative number in the real numbers, so the solutions are non-real and come in complex conjugate pairs: x = (-b ± i sqrt(|Δ|)) / (2a). This means there are no real roots, only complex ones. The other scenarios give two real roots when Δ > 0, or a single real (double) root when Δ = 0.

If Δ > 0, the roots are complex.