What are all the possible rational zeros for #f(x)=4x^4-17x^2+4# and how do you find all zeros?

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Answer 1 · 2016-10-07T19:50:06

#"All the "4# possible zeroes of #f" "are, +-1/2,+-2.#

#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.#