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Number and Type of Solutions of a Quadratic Equation Based on the Discriminant
The value of the discriminant, , reveals the number and type of solutions for a quadratic equation (where ), without requiring the equation to be fully solved:
- If (positive discriminant), the equation has two real solutions.
- If (zero discriminant), the equation has one real solution.
- If (negative discriminant), the equation has two complex solutions (meaning it has no real solutions).
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