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

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Answer 1 · 2016-10-07T19:50:06

$All the 4$ $"All the "4$ possible zeroes of $f a r e, \pm \frac{1}{2}, \pm 2 .$ $f" "are, +-1/2,+-2.$

$f (x) = 4 x^{4} - 17 x^{2} + 4$ $f(x)=4x^4-17x^2+4$

To complete the square $4 x^{4} + 4,$ $4x^4+4,$ we find the Middle Term $= 8 x^{2} .$ $=8x^2.$

$:. f(x)=4x^4+8x^2+4-25x^2$

$=(2x^2+2)^2_(5x)^2$

$=(2x^2+5x+2)(2x^2-5x+2)$

$={ul(2x^2+4x)+ul(x+2)}{ul(2x^2-4x)-ul(x+2)}$

$={2x(x+2)+1(x+2)}{2x(x-2)-1(x-2)}$

$=(x+2)(2x+1)(x-2)(2x-1)$

$:." all the "4$ possible zeroes of $f" "are, +-1/2,+-2.$

What are all the possible rational zeros for f(x)=4x^4-17x^2+4f(x)=4x4−17x2+4f(x)=4x^4-17x^2+4 and how do you find all zeros?