Graph each of the following functions. Verify that each function has the given equal roots.
f(x)= 3x³ - 4x²; two roots that equal 0
I have graphed it, but what else am I supposed to do?
you have provided only a function which can not have a root. i suppose you wanted to say the roots of the equation $\displaystyle 3x^3 - 4x^2 = 0$. in that case, the graph will be like this:-http://www4d.wolframalpha.com/Calcul...20&w=300&h=187
clearly, you get the solutions from $\displaystyle x^2 (3 x-4) = 0$ ,ie, $\displaystyle x=0, x=0$ and $\displaystyle 3x-4=0,ie, x=4/3$
thus, the equation has 3 roots, 2 of which are 0, and the third one is $\displaystyle \frac{4}{3}$
Since you have the graph you should observe that the graph is tangent to the x-axis at x= 0 while it crosses the x-axis at 4/3. The fact that the graph touches or crosses the x-axis tells you that the equation has a root (and the function has a "zero") at that point. The fact that the graph is tangent to the x-axis there tells you that it has a double (or higher) root.