This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Example 1 Example 2 2 Solving Quadratic Equations with NEGATIVE Dis-criminants 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 2-4 ac 2 a (1) Let D = b 2-4 ac be the discriminant : 2 D > 0: 2 REAL solutions (2 x-intercepts) D = 0: 1 REAL REPEATED/ DOUBLED solution (1 x-intercept) D < 0: 2 COMPLEX (NOT REAL) solutions (0 x-intercept). In this case, the solutions are CONJUGATES of each other . It means that if a quadratic function of real coecients 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...
View Full Document