Lesson15 - MA 15200 I The Discriminant Lesson 15 Section...

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1 MA 15200 Lesson 15 Section 1.5 (part 2) I The Discriminant The part of the quadratic formula under the radical sign 2 ( 4 ) b ac - is called the discriminant. (Some textbooks call it the determinant.) Note: The discriminant is without the radical sign. 1. If 2 4 0 b ac - = , then the formula would be 0 2 2 b b x a a - ± = = - . There will only be one rational solution. 2. If 2 4 b ac - equals a positive perfect square number, then the formula would be 2 2 2 b k b k x a a - ± - ± = = , where k is a positive rational number. There will be two rational solutions. 3. If 2 4 b ac - equals a positive non-perfect square number, then the formula would be 2 b n x a - ± = , where n is a non-perfect square number. There will be two conjugate irrational solutions because the solutions include a radical. 4. If 2 4 b ac - equals a negative number, then the formula will be 2 2 2 b n b n x i a a a - ± - - = = ± , where n is a positive number. There will be two conjugate complex solutions. Ex 1:
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Lesson15 - MA 15200 I The Discriminant Lesson 15 Section...

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