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.
Answer (2)
The discriminant of a quadratic equation determines the nature of its roots.
A negative discriminant indicates complex roots.
Since the discriminant is -8, the quadratic equation has two complex roots.
The answer is: There are two complex roots.
Explanation
Understanding the Discriminant The discriminant of a quadratic equation determines the nature of its roots. The discriminant, denoted as D , is given by the formula D = b 2 − 4 a c for a quadratic equation of the form a x 2 + b x + c = 0 .
Interpreting the Discriminant's Value If 0"> D > 0 , the equation has two distinct real roots. If D = 0 , the equation has one real root (or two equal real roots). If D < 0 , the equation has two complex conjugate roots.
Applying the Given Discriminant In this problem, the discriminant is given as D = − 8 . Since − 8 < 0 , the quadratic equation has two complex roots.
Conclusion Therefore, the correct statement is: There are two complex roots.
Examples
Consider a scenario where you're designing an electrical circuit and need to find the values of components that satisfy a certain equation. If the discriminant of that equation is negative, it tells you that the solutions are complex numbers, which might indicate that the circuit will oscillate or have a reactive component. Understanding the nature of roots helps engineers design stable and efficient systems.
Since the discriminant is − 8 , which is less than zero, the quadratic equation has two complex roots. The correct answer is: There are two complex roots.
;
