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can you please tell me what i did wrong?

Find the zeroes if any of the rational function g(x)=x^3-125/x^2+1
TTHIS IS WHAT I DID
g(x)=x^3-125/x^2+1
      x^3-125=0
       (x-5)(x^2+5x+25)
Because x^2+1can not be factor 
The zero of this rational function is x=5
        

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Meena S. | Patient & knowledgeable Mathematics & Statistics (SPSS) TutorPatient & knowledgeable Mathematics & St...
4.5 4.5 (56 lesson ratings) (56)
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Hi Daisy,
g(x)=x^3-125/x^2+1
      =(x-5)(x^2+5x+25)
now we can find complex roots for (x^2+5x+25),
 
x^2+5x+25=0
using formula,if ax^2+bx+c=0,
then x= -b ±√b²-4ac ⁄ 2a
substituting a= 1, b= 5, c= 25, we get,
 
x= -5±√5²-4(1)(25)/ 2(1)
  =-5 ±√25-100/2
  =-5 ± √-75 /2.............(√-75=√25*3*-1=5√3 i  as √-1=i)
x= -5+5√3 i /2  or x= -5-5√3 i /2
 
Denominator cannot be equal to zero.
 
Ans: zeros are 5, -5+5√3 i/2, -5-5√3 i /2
 
Meena from Strongsville,OH