Question

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

• If \(D>0\), two distinct real roots.
• If \(D = 0\), one real root (double root).
• If \(D<0\), two complex conjugate roots.

Step2: Analyze given discriminant

Given \(D = 4\), which is \(>0\). So, two distinct real roots.

Answer:

There are two real roots.