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how to find all real and imaginary zeros of f(x)=x^4+5x^2-5x^3-6+5x

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luana
[tex]f(x)=x^4+5x^2-5x^3-6+5x\\\\ Sorting\ equation:\\ f(x)=x^4-5x^3+5x^2+5x-6\\\\ Write\ 5x^2\ as\ -x^2+6x^2\ \ to\ factor\ equation:\\\\ f(x)=x^4-5x^3+-x^2+6x^2+5x-6\\ f(x)=x^2(x^2-1)-5x(x^2-1)+6(x^2-1)\\ f(x)=(x^2-5x+6)(x^2-1)\\ From\ first\ bracket\ write\ -5x\ as\ -2x-3x\\ f(x)=(x^2-2x-3x+6)(x^2-1)\\ f(x)=(x(x-2)-3(x-2))(x-1)(x+1)\\ f(x)=(x-2)(x-3)(x-1)(x+1)\\\\ To\ find\ roots\ compare\ equation\ to\ 0:\\ (x-2)(x-3)(x-1)(x+1)=0\\ x-2=0\ \ or\ \ x-3=0\ \ or\ \ x-1=0\ \ or\ \ x+1=0 [/tex][tex]x=2\ \ or\ \ x=3\ \ or\ \ x=1\ \ or\ \ x=-1.\\\\ Solution:\\ x\in\{-1,1,2,3\}[/tex]
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