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?

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Q: sider the following quadratic form on R²:

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Q: Are there any complex solutions to the equation 2x² - 19x x2 – 5x = x - 3? If so, what are they?

A: see below the solution