What are all the possible rational zeros for #f(x)=4x^4-17x^2+4# and how do you find all zeros? Precalculus Real Zeros of Polynomials Rational Zeros 1 Answer Ratnaker Mehta Oct 7, 2016 #"All the "4# possible zeroes of #f" "are, +-1/2,+-2.# Explanation: #f(x)=4x^4-17x^2+4# To complete the square #4x^4+4,# we find the Middle Term#=8x^2.# #:. f(x)=4x^4+8x^2+4-25x^2# #=(2x^2+2)^2_(5x)^2# #=(2x^2+5x+2)(2x^2-5x+2)# #={ul(2x^2+4x)+ul(x+2)}{ul(2x^2-4x)-ul(x+2)}# #={2x(x+2)+1(x+2)}{2x(x-2)-1(x-2)}# #=(x+2)(2x+1)(x-2)(2x-1)# #:." all the "4# possible zeroes of #f" "are, +-1/2,+-2.# 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 #x^3-7x-6#? 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? See all questions in Rational Zeros Impact of this question 3470 views around the world You can reuse this answer Creative Commons License