Question 1127284: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -2, 2-i
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source):
Answer by ikleyn(52794)  (Show Source):
You can put this solution on YOUR website! .
For any polynomial with real coefficients, the roots go in pairs (complex number, conjugate complex number).
Therefore, at given condition, the roots of the polynomial are -2, 2-i and 2+i,
and one possible polynomial is THIS
f(x) = (x+2)*(x-(2-i))*(x-(2+i)), which is the same as
f(x) = (x+2)*((x-2)+i)*((x-2)-i) = (x+2)*((x-2)^2+1).
For your safety, ignore the post by @josgarithmetic, since it is W R O N G, as usual.
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