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If is the only -intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
The discriminant is negative.
The discriminant is -3 .
The discriminant is 0 .
The discriminant is positive.
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Studdy Solution
STEP 1
1. The quadratic equation has the form .
2. The -intercept occurs where the quadratic equation equals zero.
3. The discriminant of a quadratic equation is given by .
4. The nature of the roots of the quadratic equation is determined by the discriminant:
- If the discriminant is positive, there are two distinct real roots.
- If the discriminant is zero, there is exactly one real root (a repeated root).
- If the discriminant is negative, there are no real roots (complex roots).
STEP 2
1. Analyze the given information about the -intercept.
2. Determine the implications for the discriminant.
3. Select the correct statement about the discriminant.
STEP 3
Analyze the given information. Since is the only -intercept, the quadratic equation has exactly one real root at .
STEP 4
Determine the implications for the discriminant. If there is exactly one real root, the discriminant must be zero because a zero discriminant indicates a repeated root.
STEP 5
Select the correct statement about the discriminant. Based on the analysis, the discriminant is .
The statement that best describes the discriminant of the equation is:
The discriminant is 0.
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