A cubic equation with real coefficients has 2 + 3i as one root. Which of these must also be a root?
Answer and explanation
Correct answer: A. 2 - 3i
- Step 1: Non-real roots of a polynomial with real coefficients come in conjugate pairs, so 2 - 3i is also a root. Answer: 2 - 3i. Why not the others: -2 + 3i and -2 - 3i change the real part, and 3 + 2i swaps the parts; none of these is the conjugate.
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