What are all the rational zeros of #x^3-7x-6#?

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Answer 1 · 2018-05-21T12:03:52

Zeros are #x=-1, x=-2 and x=3#

#f(x)=x^3-7 x - 6 ; # By inspection #f(-1)=0# ,so

#(x+1)# will be a factor.

# x^3-7 x - 6 = x^3 + x^2 -x^2 -x -6 x -6#

#= x^2(x + 1) -x(x+1) -6( x +1)#

#= (x + 1)(x^2 -x -6)= (x + 1)(x^2 -3 x +2 x-6)#

#= (x + 1){x(x -3)+2( x-3)}#

#:. f(x)= (x + 1)(x -3)(x+2) :. f(x)# will be zero

for #x=-1, x=-2 and x=3#

Hence zeros are #x=-1, x=-2 and x=3# [Ans]