can you please tell me what i did wrong?

Question

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

        

Answer 1

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