How do you find all the zeros of #x^3-3x^2-x+3# with 3 as a zero?

1 Answer

Answer:

The zeros are #x=3# and #x=-1# and #x=+1#

Explanation:

By synthetic division, arrange the numerical coefficients according to degree(from highest to lowest)

#x^3" " " " " "x^2" " " " " "x^1" " " " " "x^0#

#1" " " "-3" " " "-1" " " " " " "3" " " " " "|__underline( 3 )#
#underline(" " " " " " " 3" " " " " " " 0" " " " "" " -3#
#1" " " " " "0" " " " " -1" " " " " " " 0" " "larr#the remainder

Our depressed equation is now

#x^2+0*x-1=0#

which is reduced by 1 degree from degree 3.
Solve for the remaining roots

#x^2-1=0#

#x^2=1#

#sqrt(x^2)=+-sqrt(1)#

#x=-1# and #x=+1#

God bless...I hope the explanation is useful