33. Four roots of a polynomial are 2, 4 + i, 5 – 3i, and –2i. Which number is NOT necessarily a root of the equation?
A. -2
B. 5 + 3i
C. 2i
D. 4 – i
A. -2
B. 5 + 3i
C. 2i
D. 4 – i
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If a polynomial has real coefficients, then for any complex root a+ib, there must exist a second root which is the somplex conjugate of the first (a - ib).
However, having 2 as a root does not imply that -2 is also a root, as the complex conjugate of 2 is also 2, and we already know that is a root.
However, having 2 as a root does not imply that -2 is also a root, as the complex conjugate of 2 is also 2, and we already know that is a root.