Question 992993: please help me with Find a polynomial f(x) of degree 3 with real coefficients and the following zeros: 4, -1+i
First change the signs on (x-(-1+i) and (x+(-1+i).
giving me (x+1+i) and (x-1+i)
I then disturbed and is left with (x^2+2xi-2)
Then i disturbed the (x-4): (x^3+2ix^2-2x-4x^2-8xi+8)
That is when i get confused.
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Answer by ikleyn(52868)   (Show Source):
You can put this solution on YOUR website! .
Wrong.
Your polynomial should be with real coefficients.
Then, having the root -1+i, it must have the conjugated complex number -1-i as the other root.
So the roots must be 4, -1+i and -1-i.
Hence, the polynomial is (x-4)*(x-(-1+i))*(x-(-1-i)).
You can transform it further, if you want.
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