SOLUTION: Complex zeros of a polynomial function for a starting point write the polynomial f(x)=x^4+12x^3-9x^2+48x-52

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Question 1063301: Complex zeros of a polynomial function for a starting point write the polynomial f(x)=x^4+12x^3-9x^2+48x-52
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
Read your post and try to understand for what reason did you send it.


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Are you looking for all complex zeros of f(x)? What were you given? You show a function polynomial in general form. Use synthetic division and Rational Roots Theorem to check possible rational roots, first. You can choose from among the positive and negative of 1, 2, 4, 13, 26, 52.


RATIONAL ROOT RESULTS WHICH WORKED 

1    |    1    12    -9    48    -52
     |
     |         1    13      4     52
     ---------------------------------
         1    13    4     52     0

Linear factor  (x-1).


-13   |   1    13    4    52
      |       -13    0    -52
      ---------------------------
         1     0     4    0

Linear factor  x+13, and quadratic factor x^2+4


The complex zeros having imaginary parts are based on x%5E2%2B4=0;
x%5E2=-4
x=0%2B-+sqrt%28-4%29
x=0%2B-++2%2Asqrt%28-1%29
highlight%28system%28x=-2i%2Cx=2i%29%29

The other two zeros are rational, being -13 and 1.