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If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?

A. There are two complex roots.
B. There are two real roots.
C. There is one real root.
D. There is one complex root.

Sagot :

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To determine the nature of the roots of a quadratic equation, we rely on the value of its discriminant. The discriminant [tex]\(\Delta\)[/tex] of a quadratic equation of the form [tex]\(ax^2 + bx + c = 0\)[/tex] is given by the formula:

[tex]\[ \Delta = b^2 - 4ac \][/tex]

The value of the discriminant can tell us the nature of the roots of the quadratic equation:

1. If [tex]\(\Delta > 0\)[/tex], the quadratic equation has two distinct real roots.
2. If [tex]\(\Delta = 0\)[/tex], the quadratic equation has exactly one real root (or a repeated real root).
3. If [tex]\(\Delta < 0\)[/tex], the quadratic equation has two complex conjugate roots.

In this specific problem, we are given that the discriminant [tex]\(\Delta\)[/tex] of the quadratic equation is equal to [tex]\(-8\)[/tex]. Therefore, [tex]\(\Delta < 0\)[/tex], which implies that the quadratic equation has two complex roots.

Thus, the correct statement that describes the roots is:

- There are two complex roots.
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