A quadratic equation is given by . Calculate the discriminant and determine the nature of the roots. The discriminant is ______, indicating that the roots are ________.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to calculate the discriminant of a quadratic equation and determine the nature of its roots. The given quadratic equation is .
Key Concept Explanation
The discriminant of a quadratic equation is given by . The value of the discriminant determines the nature of the roots:
If , there are two distinct real roots.
If , there is exactly one real root (a repeated root).
If , there are two complex conjugate roots.
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