How do you find the zeroes of # f(x)= x^3 - 17x^2 + 81x -65#?

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Answer 1 · 2018-03-03T12:43:45

Zeros are #x=1 , x= 8-1i and x= 8+1i #

#f(x)=x^3-17x^2+81x-65 # or

#f(x)=x^3-x^2-16x^2+16x+65x-65 # or

#f(x)=x^2(x-1)-16x(x-1)+65(x-1)# or

#f(x)=(x-1)(x^2-16x+65) :. x=1# is one zero

#f(x)= x^2-16x+65 # or

#f(x)= x^2-16x+64 +1 # or

#f(x)= (x-8)^2 - (i^2) [i^2=-1]# or

#f(x)= (x-8+ i)(x-8-i) :. #. Other zeros are

#x= 8-1i and x= 8+1i #

Zeros are #x=1 , x= 8-1i and x= 8+1i # [Ans]