How do you find all zeros for #x^3 - 5x^2 + x - 5#?

1 Answer
Alan P.
May 17, 2016

#x =5#
or
#x=+-i#

Explanation:

#x^3-5x^2+x-5# can be factored as
#color(white)("XXX")color(red)(""(x^3+x))-color(blue)(""(5x^2+5))#

#color(white)("XXX")=color(red)(x(x^2+1))-color(blue)(5(x^2+1)#

#color(white)("XXX")=(color(red)(x)-color(blue)(5))*(x^2+1)#

For the zeroes:
either
#color(white)("XXX")(x-5)=0color(white)("XX")rarrcolor(white)("XX")x=5#
or
#color(white)("XXX")(x^2+1)=0color(white)("XX")rarrcolor(white)("XX")x=+-sqrt(-1)=+-i#

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