How do you find all the zeroes of #x^4-6x^2-7x-6=0#, if #x=3# and #x=-2#?

1 Answer
Cem Sentin
Feb 19, 2018

#x_1=3#, #x_2=-2#, #x_3=Cis120# and #x_4=Cis240#

Explanation:

#x^4-6x^2-7x-6=0#

#x^4-3x^3+3x^3-9x^2+3x^2-9x+2x-6=0#

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

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

#(x-3)(x+2)(x^2+x+1)=0#

Hence root of this polynomial are #x_1=3#, #x_2=-2#, #x_3=-1/2+(sqrt3)/2*i=Cis120# and #x_4=-1/2-(sqrt3)/2*i=Cis240#

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