How many real roots does the equation (9x^5)-(4x^4)+(8x^3)-4x+1=0 have?

[wildcat12]

Homework Statement

Show that the equation (9x^5)-(4x^4)+(8x^3)-4x+1=0 has exactly 3 real roots.

Homework Equations

The Attempt at a Solution

I found a derivative of (45x^4)-(16x^3)+(24x^2)-4. I am not sure how to set this equal to zero

 

[hunt_mat]

Use the intermediate value theorem, if f(x) is a continuous function and there exist point a<b such that f(a)<0<f(b) or f(a)>0>f(b) then there is a point c, where f(c)=0.

My advice is to plot the graph and find approximatly where they are and then use the above to prove it so.

 

[vela]

Also, you should show there's only one inflection point, so you have only 3 roots and not 5.