SOLUTION: Use the given zero to find the remaining zeros of the function. f(x)=x^4-18x^3+78x^2+294x-3355 zero; 6-5i

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Question 690752: Use the given zero to find the remaining zeros of the function.
f(x)=x^4-18x^3+78x^2+294x-3355 zero; 6-5i

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!



If 6 - 5i is a zero, then 6 + 5i must also be a zero.  Therefore both [x - (6 - 5i)] and [x - (6 + 5i)] are factors of the given polynomial function.


Multiply the two factors to get x2 - 12x + 61, which, since it is a composite of two factors of the given polynomial must also be a factor of the given polynomial.


Use polynomial long division to find the other quadratic factor of the given quartic:

                              x2 -   6x -   55
              ---------------------------------
x2 - 12x + 61 | x4 - 18x3 + 78x2 + 294x - 3355
                x4 - 12x3 + 61x2
              -------------------------
                   -  6x3 + 17x2 + 294x
                   -  6x3 + 72x2 - 366x
                   ---------------------------
                          - 55x2 + 660x - 3355
                          - 55x2 + 660x - 3355
                         ---------------------
                                             0

Finally, factor  x2 - 6x - 55 = (x + 5)(x - 11) from which you can get your final two zeros.

John

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