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math help?
can you not only answer it but tell me how you did it? (my final is tomorrow)
Form a polynomial f(x), with real coefficients, having the given degree and zeros.
degree3; zeros 2 and (1+i)
1 Answer
- hayharbrLv 71 decade agoFavorite Answer
complex zeros occur in conjugate pairs, meaning if 1 + i is a zero, so is 1 - i
So take those two first; they come from a
quadratic ax^2 + bc + c where the sum of the zeros (roots) is -b/a and the product is c/a
So let a = 1 (easiest). Then -b/a = (1 + i ) + (1 - i) = 2 so b = -2
and (1+i)(1-i) = 1 - i^2 = 1+1 = 2 so c/a = 2 and c is 2
So far you have x^2 - 2x + 2
The other zero is 2 so its factor is x-2.
Multiply (x-2)(x^2 - 2x + 2) to get the final answer
Instead of the sum/product way, you could also multiply out (x - (1 + i))(x - (1 - i))
x^2 -x + xi - x - xi + 1 - i^2
which is x^2 - 2x + 1 + 1 or x^2 - 2x + 2
So whichever you were told to do, or whichever seems easier, do that.