SOLUTION: Solve by factoring--4xcubed - 28xsquared + 49x > 0

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Question 22955: Solve by factoring--4xcubed - 28xsquared + 49x > 0
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
First you need to figure out where 4x%5E3+-+28x%5E2+%2B+49x+=+0. So, lets do this...

x%284x%5E2+-+28x+%2B+49%29+=+0

so either x=0 or 4x%5E2+-+28x+%2B+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%28300%2C+300%2C+-1%2C+7%2C+-10%2C+30%2C+4x%5E3+-+28x%5E2+%2B+49x%29

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.