Find an upper bound and a lower bound for the zeros of the following polynomial function:
h(x)=x^4+2x^3-11x^2-14x+24

Question

Find an upper bound and a lower bound for the zeros of the following polynomial function:
h(x)=x^4+2x^3-11x^2-14x+24

anonymous · Answer

Try this:
Starting at 0, move out to $$\pm1\pm2\pm3$$and so on.
You should see 4 changes of signs.  (I cheat ) From plotting the graph, you should see the 4 change of signs within -4 and +3.

anonymous · Answer

Anybody has other suggestion?

anonymous · Answer

To determine how many times the curve crosses the x axis, differentiate and equate to 0.  In this case you should see that of the 3 max/min points, 2 will be on one side of the x axis and one will be on the other side.  So we conclude that the curve will cross the x axis 4 times hence the 4 change of signs.

anonymous · Answer

@sourwing any comment

anonymous · Answer

I am not allowed to use a graphing calculator in this section of the homework. I made a list of all the possible zeros and started testing them. I got the upper bound correct (4), but I can't seem to find the lower bound.

anonymous · Answer

Have you moved to -4?

anonymous · Answer

What class are you doing?

anonymous · Answer

There should be a change of sign between -2 and -3 and again between -3 and -4.

anonymous · Answer

I am in Pre-Calculus. It is an online course, so the homework answers are given. I just can't figure out how they got to it. The lower bound is said to be -6, but I don't understand why that is.

anonymous · Answer

Apart from giving the suggestions above, I am stumped.

anonymous · Answer

Okay, thank you anyway!