Problem 132 of 7
Explain why nonreal roots occur in conjugate pairs for real polynomials in only one nonreal root listed for a real quadratic.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
connect conjugate multiplication to real coefficients.
Hidden until you reveal it.
Explanation must connect conjugates to real coefficients or conjugating the equation.
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Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. State the polynomial has real coefficients.
2. Use conjugate-factor multiplication or conjugation of equation.
3. Conclude nonreal roots appear in conjugate pairs.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Claiming conjugates are needed for all complex-coefficient polynomials.