The discriminant of a quadratic equation is b^2 - 4ac. What does it tell us about the roots?

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Multiple Choice

The discriminant of a quadratic equation is b^2 - 4ac. What does it tell us about the roots?

Explanation:
The discriminant b^2 - 4ac tells you how many real roots a quadratic has. If it’s positive, there are two distinct real roots. If it’s zero, there’s one real root (a repeated root). If it’s negative, there are no real roots (the solutions are complex). So it directly answers the number of real solutions, rather than the sum of the roots or any particular coefficient value. For example, x^2 - 5x + 6 has D = 25 - 24 = 1 > 0, so two real roots; x^2 + 2x + 1 has D = 4 - 4 = 0, so one real root; x^2 + 2x + 5 has D = 4 - 20 = -16, so no real roots.

The discriminant b^2 - 4ac tells you how many real roots a quadratic has. If it’s positive, there are two distinct real roots. If it’s zero, there’s one real root (a repeated root). If it’s negative, there are no real roots (the solutions are complex). So it directly answers the number of real solutions, rather than the sum of the roots or any particular coefficient value. For example, x^2 - 5x + 6 has D = 25 - 24 = 1 > 0, so two real roots; x^2 + 2x + 1 has D = 4 - 4 = 0, so one real root; x^2 + 2x + 5 has D = 4 - 20 = -16, so no real roots.

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