Quadratically complex (really)!
What is the lowest degree of a polynomial with rational coefficients if one of its root is ?
Note: is the imaginary unit.
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1 solution
If 2 + i is one root, 2 − i must be another root. The equation having these as roots is given by
x 2 − 2 2 x + 3 = 0 2 2 x = x 2 + 3 .
Since the coefficients need to be rational, squaring both sides we get a fourth degree equation.