Question 1100952: Using the given zero, find one other zero of f(x).
3 - 6i is a zero of f(x).= x^4 - 6x^3 + 46x^2 - 6x + 45.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Using the given zero, find one other zero of f(x).
3 - 6i is a zero of f(x).= x^4 - 6x^3 + 46x^2 - 6x + 45.
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Since f(x) has Real Number coefficients, 3+6i is also a zero
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So f(x) is divisible by ((x-3)+6i)((x-3)-6i) = (x-3)^2+36 = x^2-6x+45
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Divide f(x) by x^2-6x+45 to get x^2+1
But x^2+1 = (x+i)(x-i)
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Answer:: i and -i are zeroes
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Cheers,
Stan H.
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