Problem 124 of 7
Explain why real-coefficient quadratic x^2-4x+13=0 has complex roots in conjugate pairs.
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connect formula structure to +/- imaginary part.
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Quadratic must have real coefficients and negative discriminant.
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Solution
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1. Start from the quadratic formula.
2. A negative discriminant becomes an imaginary term.
3. The plus/minus produces a+bi and a-bi.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Saying conjugates occur by coincidence.