Under what condition does a quadratic equation ax^2 + bx + c = 0 have equal roots?
Answer and explanation
Correct answer: B. b^2 - 4ac = 0
- Step 1: In the quadratic formula x = (-b +- sqrt(b^2 - 4ac)) / 2a, the +- term vanishes when the discriminant is zero. Step 2. Thus b^2 - 4ac = 0 results in a single repeated root x = -b / (2a). Answer: b^2 - 4ac = 0. Why not the others: b^2 - 4ac > 0 produces two distinct real roots; b^2 - 4ac < 0 produces complex conjugate roots; b = 0 gives symmetric roots +-sqrt(-c/a).
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