bkartch
Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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

Sagot :

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]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.