SOLUTION: f(x)=x^4+10x^3+27x^2+10x+26; if i is a zero, find the other three.

i | 1 10    27      10      26
  |     +i  -1+10i -10+26i -26
    1 10+i  26+10i     26i   0

So we have factored f(x) this way

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Since i, that is, (0+i), is a zero, so is its conjugate (0-i), or -i

So we factor further by using synthetic division to factor the
expression in brackets:

-i | 1  10+i  26+10i  26i
   |      -i    -10i -26i  
     1  10    26        0

So we have factored f(x) this way



Set the last factor = 0



That does not factor so we use the quadratic formula:















So the four zeros are , , , and 

Edwin