Question

f(x)=x^​6-​10*​x^​5-​7*​x^​4+​80*​x^​3+​12*​x^​2-​192*​x
how to find the answer an its graph???

Answer 1

y = x^​6-​10​x^​5-​7​x^​4+​80​x^​3+​12​x^​2-​192​x
= x(x^​5-​10​x^4-​7​x^3+​80​x^2+​12​x-​192​)

you know any rational roots will be factors of 192. There appear to be none except x=0.

If you visit wolframalpha.com and enter the formula, you will find one root near x=10, but that is the only real nonzero root.

To see what happens near x=0, try visiting

http://rechneronline.de/function-graphs/

set the x range -10 to 10
y -1000 to 1000