How do you find the rest of the zeros given one of the zero c=1 and the function #f(x)=x^3-6x^2+11x-6#?

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Answer 1 · 2016-08-22T18:54:27

Other zeros are #2# and #3#.

#f(x)=x^3-6x^2+11x-6# has one of the zeros as #1#, #(x-1)# is factor of #f(x)#.

Dividing #f(x)=x^3-6x^2+11x-6# by #(x-1)#, we get #x^2(x-1)-5x(x-1)+6(x-1)# or

#(x-1)(x^2-5x+6)#, which can be further factorized as

#(x-1)(x^2-3x-2x+6)#

= #(x-1)(x(x-3)-2(x-3))#

= #(x-1)(x-2)(x-3)#

Hence, other zeros are #2# and #3#.