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Question

Find the quadratic polynomial, with real coefficients, which has 3 + i as a root, and where the coefficient of x^2 is 2.

Accepted Answer

Since the polynomial has real coefficients, the other root must be 3 - i. Thus, the polynomial is align* 2(x - 3 - i)(x - 3 + i) &= 2((x - 3)^2 - i^2) &= 2((x - 3)^2 + 1) &= 2x^2 - 12x + 20. align*