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12. Consider the quadratic equation az?+bz+c= 0, where a, b and c are real and b2 – 4ac < 0. Suppose that w is one of the complex roots of the equation. (a) Explain why aw? + bw + c = 0. (b) By taking the conjugate of both sides of the result in (a), and using the properties of conjugates, show that a (w)² + bū+c= 0. (c) What have you just proved about the two complex roots of the equation?

12. Consider the quadratic equation az?+bz+c= 0, where a, b and c are real and b2 – 4ac < 0. Suppose that w is one of the complex roots of the equation. (a) Explain why aw? + bw + c = 0. (b) By taking the conjugate of both sides of the result in (a), and using the properties of conjugates, show that a (w)² + bū+c= 0. (c) What have you just proved about the two complex roots of the equation?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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12. Consider the quadratic equation az+bz+c= 0, where a, b and c are real and b² – 4ac < 0. Suppose that w is one of the complex roots of the equation. (a) Explain why aw? + bw + c = 0. (b) By taking the conjugate of both sides of the result in (a), and using the properties of conjugates, show that a (w) +bw+c= 0. (c) What have you just proved about the two complex roots of the equation? 2
Transcribed Image Text:12. Consider the quadratic equation az+bz+c= 0, where a, b and c are real and b² – 4ac < 0. Suppose that w is one of the complex roots of the equation. (a) Explain why aw? + bw + c = 0. (b) By taking the conjugate of both sides of the result in (a), and using the properties of conjugates, show that a (w) +bw+c= 0. (c) What have you just proved about the two complex roots of the equation? 2
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