How do you find the roots of #x^3+x^2-17x+15=0#?

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Answer 1 · 2016-09-23T21:12:33

The roots are: #x=1#, #x=-5# and #x=3#

#x^3+x^2-17x+15 = 0#

Note that the sum of the coefficients is #0#. That is:

#1+1-17+15 = 0#

So #x=1# is a root and #(x-1)# a factor:

#0 = x^3+x^2-17x+15#

#color(white)(0) = (x-1)(x^2+2x-15)#

Then note that #5*3=15# and #5-3=2#, so

#x^2+2x-15 = (x+5)(x-3)#

So the other two roots are #x=-5# and #x=3#