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Unformatted text preview: Example 1 Example 2 2 Solving Quadratic Equations with NEGATIVE Discriminants Quadratic Formula : In the complex number system, the solutions of a quadratic equation ax 2 + bx + c = 0, where a 6 = 0 , a, b, c are real numbers can be computed by the quadratic formula: x =b ± √ b 24 ac 2 a (1) Let D = b 24 ac be the discriminant : 2 • D > 0: 2 REAL solutions (2 xintercepts) • D = 0: 1 REAL REPEATED/ DOUBLED solution (1 xintercept) • D < 0: 2 COMPLEX (NOT REAL) solutions (0 xintercept). In this case, the solutions are CONJUGATES of each other . It means that if a quadratic function of real coeﬃcients has a complex number z as a zero, then the complex conjugate ¯ z is also a zero. Remark : √1 = i ⇒ √16 = √1 √ 16 = 4 i . Example 3 3...
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 Spring '11
 Nuegyen
 Equations, Complex Numbers, Quadratic equation, Complex number, real solutions

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