If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?
Question
If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?
Solution
The quadratic equation will have exactly one real solution. This is because the discriminant (b² - 4ac) of a quadratic equation (ax² + bx + c = 0) determines the nature of the roots of the equation. If the discriminant equals zero, it means that the equation has exactly one real root (also known as a repeated root). This is because the roots of a quadratic equation are given by the formula (-b ± √(b² - 4ac)) / 2a. If the discriminant is zero, then the square root term disappears, and the equation has only one solution: -b / 2a.
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