Question Find the discriminant of a quadratic equation with as the only -intercept. The discriminant is 0.
Studdy Solution
STEP 1
Assumptions
1. The graph of the quadratic equation has as its only -intercept.
2. The quadratic equation is in the form .
3. The discriminant of a quadratic equation is given by .
4. The discriminant determines the nature and number of the roots of the quadratic equation.
STEP 2
Understand the relationship between the discriminant and the roots of a quadratic equation.
1. If the discriminant is positive, the quadratic equation has two distinct real roots.
2. If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).
3. If the discriminant is negative, the quadratic equation has no real roots, but two complex roots.
STEP 3
Since the graph of the quadratic equation has as its only -intercept, it means that the quadratic equation has exactly one real root, which is . This implies that the root is repeated.
STEP 4
Relate the information about the root to the discriminant of the quadratic equation.
Since the quadratic equation has exactly one real root, the discriminant must be zero.
STEP 5
Conclude the value of the discriminant based on the given information.
The discriminant of the quadratic equation is 0.
The statement that best describes the discriminant of the equation is: The discriminant is 0.
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