Solved on Dec 05, 2023
If the discriminant of an equation is positive, the equation has .
STEP 1
Assumptions
1. We are dealing with a quadratic equation of the form .
2. The discriminant of a quadratic equation is given by .
3. The nature of the roots of the quadratic equation depends on the value of the discriminant.
STEP 2
Recall the relationship between the discriminant () and the nature of the roots of a quadratic equation.
1. If , the quadratic equation has two distinct real solutions.
2. If , the quadratic equation has exactly one real solution (a repeated real root).
3. If , the quadratic equation has two complex solutions.
STEP 3
Since the discriminant of the equation is given to be positive (), we can conclude that the quadratic equation has two distinct real solutions.
STEP 4
Match our conclusion with the given options.
The correct option that matches our conclusion is:
D. It has two real solutions.
The discriminant being positive indicates that the quadratic equation has two distinct real solutions.
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