Question

Prove that the function:
(x^4-x^3+x^2-x-2)/(x^2+x+1)
crosses the x-axis somewhere between -1 and 1.

Answer 1

forget the denominator, it is never zero. check that the numerator is positive for one value and negative for another. since the denominator is always positive, that means it crosses the x axis between -1 and 1

Answer 2

satellite has it. :)

You can show that the denominator is never zero by showing its roots are complex by using the quadratic formula.

I've attached a picture of your function (made with geogebra).

Answer 3

how do u use the quadratic formula with a quartic?

Answer 4

oh nvm the denominator