What are all the rational zeros of #x^3-7x-6#? Precalculus Real Zeros of Polynomials Rational Zeros 1 Answer Binayaka C. May 21, 2018 Zeros are #x=-1, x=-2 and x=3# Explanation: #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] Answer link Related questions What is the rational zeros theorem? How do I find all the rational zeros of function? What is a rational zero? How do I find all the rational zeros of a function like #f(x)=x^3-7x-6#? How do you find all the rational zeros of a polynomial function? How do I find all the rational zeros of #p(x)=x^3-12x-16#? What are all the rational zeros of #2x^3-15x^2+9x+22#? What are the rational zeros for #x^3-3x^2-4x+12#? What are the rational zeros of a polynomial function? What is the rational zeros test? See all questions in Rational Zeros Impact of this question 10484 views around the world You can reuse this answer Creative Commons License