Often times we have to solve a polynomial equation that we can't solve by factoring. So what I have behind me is a cubic equation that we're trying to solve. We don't have the tools to do this algebraically so what we're going to have to do is go to a calculator and I'm going to show you how to go to a calculator, plug this in and find your answer.
So once we have our calculator, what we want to go to is the y equals button. So we have our y equals and then we want to write in the equation that we're concerned with. The x variable is represented by this xt theta n button so you have your x to the third minus 4x plus 7 and then just say graph and we get this picture right here.
So what we're looking for is where this is equal to 0, and we can see we have a 0 around -2, -3 somewhere in there, but that's not really going to give us appropriate answers, so what we have to do is calculate the 0 which we go to by going second calc and then you see these menu of options. We go through there and we want to calculate 0 so you can either scroll down to 0, or you can just hit the number 2, either way will give you what you want.
You then have this part that says 'Left Bound', so what you want to do is using your side to side keys, get your cursor to the left side of that 0. Once you're there just hit enter, go to the other side as now I see for the right bound, you want to make sure you're on the right side of your 0, hit enter again guess I'm not really sure what guess is doing so you can always just hit enter wherever you are and it will give you your 0 in this case we are looking at -2.589, depending on the number of significant digits your teacher is asking for, you can give them any sort of combination of those numbers.
So solving a rational equation by, solving an equation by graphing, plug it in and then do the second calc zero to find your zeros.