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How do you find all the real and complex roots of #f(x)=x^3-5x^2+11x-15#?

1 Answer

Mar 19, 2018

#x_1=3#, #x_2=1-2i# and #x_3=1+2i#

Explanation:

#x^3-5x^2+11x-15=0#

#x^3-3x^2-2x^2+6x+5x-15=0#

#x^2*(x-3)-2x*(x-3)+5*(x-3)=0#

#(x-3)*(x^2-2x+5)=0#

From first multiplier, #x_1=3#. From second one #x_2=1-2i# and #x_3=1+2i#

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