Question

if the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
there are two complex roots.
there are two real roots.
there is one real root.
there is one complex root.

Explanation:

Step1: Recall Discriminant Rules

For a quadratic equation \(ax^2 + bx + c = 0\), the discriminant is \(D = b^2 - 4ac\).

• If \(D>0\), two distinct real roots.
• If \(D = 0\), one real root (a repeated root).
• If \(D<0\), two complex conjugate roots (since \(\sqrt{D}\) is imaginary).

Step2: Analyze Given Discriminant

Given \(D=-8\), which is less than 0. So, the quadratic has two complex roots (they come in conjugate pairs, so two complex roots).

Answer:

There are two complex roots.