Question 22955
First you need to figure out where {{{4x^3 - 28x^2 + 49x = 0}}}. So, lets do this...


{{{x(4x^2 - 28x + 49) = 0}}}


so either x=0 or {{{4x^2 - 28x + 49 = 0}}}


The second polynomial factorises futher to (2x-7)(2x-7) = 0, which means 2x = 7. In other words x = 7/2.


So there are 2 "roots" (where y=0): at x=0 and x=7/2.


The question asks where is the polynomial GREATER than zero. To answer this, you need to be able to sketch (not plot) the graph quickly. You need to know what a cubic looks like first and then apply that knowledge to the info you have.


The cubic looks like: {{{graph(300, 300, -1, 7, -10, 30, 4x^3 - 28x^2 + 49x)}}}


So, looking at the graph, where is the curve GREATER than zero? it is greater than zero when x>0 but not at the point x=7/2 --> here it is equal to zero.


So, answer is 0 < x < 7/2 and x > 7/2 
OR x>0, but not x=7/2


Both say the same thing


jon.