# How do you find the roots of #x^3+x^2-5x+3=0#?

##### 1 Answer

Sep 29, 2016

The roots are:

#x=1" "# with multiplicity#2#

#x=-3" "# (with multiplicity#1# )

#### Explanation:

Note that the sum of the coefficients of

#1+1-5+3 = 0#

Hence

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

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

Hence the roots of the given equation are:

#x=1# with multiplicity#2#

#x=-3#

graph{x^3+x^2-5x+3 [-10.545, 9.455, -22.2, 27.8]}