Use the given zero to find all the zeros of the function. f(x) = x^3 + x^2 + 9x + 9 Given zero: r = 3i So, I think that I have to use synthetic division using 3i and -3i as roots? Is this right? If so, what is the next step?
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Originally Posted by tsmith Use the given zero to find all the zeros of the function. f(x) = x^3 + x^2 + 9x + 9 Given zero: r = 3i So, I think that I have to use synthetic division using 3i and -3i as roots? Is this right? If so, what is the next step? Since two of the zeros are 3i and -3i you can multiply their linear parts like so: (x-3i)(x+3i)=x^2+6i-6i-9(i^2)= x^2+9 Now synthetically divide f(x) by x^2+9 and you should get your last zero solution.
Originally Posted by tsmith Use the given zero to find all the zeros of the function. f(x) = x^3 + x^2 + 9x + 9 Given zero: r = 3i So, I think that I have to use synthetic division using 3i and -3i as roots? Is this right? If so, what is the next step? The bold is correct. So you just need one more real root. is is one factor.
factor: (x + 1)(x^2 + 9) = (x + 1)(x + 3i)(x - 3i),
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