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 3/4/2014 | Daisy from Memphis, TN | 1 Answer | 0 Votes Mark favorite Subscribe Comment
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 3/4/2014 | Meena S. Comment