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Question 845491: Find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros.
A. –8, 5i
B. 5, − (square root)7, 1 + i
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros.
A. –8, 5i
If 5i is a zero and the coefficients must be rational, -5i is also a zero.
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f(x) = (x+8)(x-5i)(x+5i) = (x+8)(x^2+25)
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B. 5, − (square root)7, 1 + i
Same reason as above::
f(x) = (x-5)(x+sqrt(7))(x-sqrt(7))((x-1)-i)((x-1)+i)
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f(x) = (x-5)(x^2-7)((x-1)^2+1)
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f(x) = (x-5)(x^2-7)(x^2+2x+2)
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Cheers,
Stan H.
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