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ax² + bx + c > 0 for every real x exactly when
Aa < 0 and b² < 4ac
Ba > 0 and b² > 4ac
Ca > 0 and b² < 4ac
Da > 0 and b = 0
Answer & Solution
Correct answer: C. a > 0 and b² < 4ac
An upward parabola with no real roots, meaning negative discriminant, never dips below the axis.
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