Question

F(x) = x ^ 4 - 6x ^ 3 + 8x ^ 2 - 21 ^ 2 the possible rational zeros

Answer 1

Explanation:

`f(x)=x^4-6x^3+8x^2-21^2\\it~ is~ of ~degree~4\\so~it~has~4 ~zeros.\\now ~we~talk~about~zeros.\\we ~check ~the ~change~of~signs.\\f(x)= + - + -\\it~has~3~changes ~of~signs\\it~ has~ 1 ~or~ 3~ real~ roots.\\f(-x)=x^4+6x^3+8x^2-21^2\\f(-x)=+ + + -\\it~has~one~change~of~sign.\\so ~it~has~one~negative~real~root.\\`

we conclude that it has two or four real roots.