How do you find all the zeros of # f(x)=x^3+x^2-5x+3#?

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Answer 1 · 2016-05-19T22:57:05

#x^3+x^2-5x+3 = (x-1)(x-1)(x+3)#

#f(x) = x^3+x^2-5x+3#

First note that the sum of the coefficients is #0#. That is:

#1+1-5+3 = 0#

So #x=1# is a zero of #f(x)# and #(x-1)# a factor:

#x^3+x^2-5x+3 = (x-1)(x^2+2x-3)#

Again note that the sum of the coefficients of #x^2+2x-3# is #0#, so there is another factor #(x-1)#

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

Putting it all together:

#x^3+x^2-5x+3 = (x-1)(x-1)(x+3)#