If an equation has two complex roots, what can be said about its discriminant?

If an equation has two complex roots, what can be said about its discriminant?

• A. It is zero
• B. It is positive
• C. It is negative
• D. It is a perfect square

Answer: (C)

In the context of quadratic equations, the discriminant plays a crucial role in determining the nature of the roots. The discriminant is calculated using the formula \( b^2 - 4ac \) from a standard quadratic equation of the form \( ax^2 + bx + c = 0 \). When the discriminant is positive, it indicates that the equation has two distinct real roots. If the discriminant is zero, the equation has exactly one real root, often referred to as a repeated root or a double root. However, when the discriminant is negative, it signifies that the quadratic equation does not intersect the x-axis at any point. As a result, the roots will not be real numbers; instead, they will be complex numbers, consisting of both a real part and an imaginary part. Thus, the presence of two complex roots directly correlates with the condition that the discriminant must be negative. This understanding of the discriminant provides valuable insight into the behavior of quadratic equations and their solutions, emphasizing its importance in determining the nature of the roots.

In the context of quadratic equations, the discriminant plays a crucial role in determining the nature of the roots. The discriminant is calculated using the formula ( b^2 - 4ac ) from a standard quadratic equation of the form ( ax^2 + bx + c = 0 ).

When the discriminant is positive, it indicates that the equation has two distinct real roots. If the discriminant is zero, the equation has exactly one real root, often referred to as a repeated root or a double root.

However, when the discriminant is negative, it signifies that the quadratic equation does not intersect the x-axis at any point. As a result, the roots will not be real numbers; instead, they will be complex numbers, consisting of both a real part and an imaginary part. Thus, the presence of two complex roots directly correlates with the condition that the discriminant must be negative.

This understanding of the discriminant provides valuable insight into the behavior of quadratic equations and their solutions, emphasizing its importance in determining the nature of the roots.