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College Algebra / Unit 4   Alg 209 short lesson, about 20 seconds

The Discriminant

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The idea

The discriminant is the expression under the quadratic formula's radical, b² − 4ac; its sign announces the nature of the solutions before any solving.

In practice

Positive 49: two real solutions. Zero, as in x² + 6x + 9: one repeated solution. Negative, as in x² + x + 1: two complex ones.

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