SOLUTION: Find the constant c such as that the denominator will divide evenly into the numerator: x^4+10x^2+c/x+i

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Question 1191677: Find the constant c such as that the denominator will divide evenly into the numerator: x^4+10x^2+c/x+i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the constant c such as that the denominator will divide evenly into the numerator:
%28x%5E4%2B10x%5E2%2Bc%29%2F%28x%2Bi%29
assuming c is real, the we also need to have x%2Bi+as a root. That means that x%5E2%2B1 must divide it

%28x%5E4%2B10x%5E2%2Bc%29%2F%28x%5E2%2B1%29.....using long division we have

______(x%5E2%2B9
(x%5E2%2B1)|x%5E4%2B10x%5E2%2Bc
.............x%5E4%2Bx%5E2
.....................9x%5E2%2Bc
.....................9x%5E2%2B9
...........................c-9->reminder must be zero, and it will be if c=9

x%5E4%2B10x%5E2%2B9=+%28x%5E3+-+i%2Ax%5E2+%2B+9x+-+9i%29%2A%28x+%2B+i%29%2B0