Question 75778
The problem is find polynomial f(x) of degree 4 that has real coefficients and zeros 2+i and -3i.
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Think of it as the reverse of completing the square>
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x = 2 + i
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x - 2 = i: subtracted 2 from both sides
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(x-2)^2 = i^2; squared both sides
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x^2 - 4x + 4 = -1: FOILed (x-2)(x-2)
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x^2 - 4x + 4 + 1 = 0; added 1 to both sides
:
x^2 - 4x + 5 = 0
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and
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x = -3i
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x^2 = 9(-1)squared both sides
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x^2 = -9
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x^2 + 9 = 0; add 9 to both sides
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Multiply (x^2 + 9) to (x^2 - 4x + 5) and you will get: 
x^4 - 4x^3 + 14x^2 - 36x + 45
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