Thread: Upper bound/Lower bound?

Ok, I know how to start this problem, but the synthetic division is confusing me a little.

Use synthetic division to verify the upper and/or lower bounds of the zeros of f.
f(x) = 2x^4 - 8x + 3
Upper bound: x = 3; Lower bound: x = -4

So the possible real zeros I think are:
plus or minus 1/2, plus or minus 1.5

Now, I am confused. Can anyone help?

Originally Posted by tsmith

Ok, I know how to start this problem, but the synthetic division is confusing me a little.

Use synthetic division to verify the upper and/or lower bounds of the zeros of f.
f(x) = 2x^4 - 8x + 3
Upper bound: x = 3; Lower bound: x = -4

So the possible real zeros I think are:
plus or minus 1/2, plus or minus 1.5

Now, I am confused. Can anyone help?

Unfortunately, our math write capabilities do not allow for synthetic division. I could do it though.

Are you have a problem with the synthetic division itself, or the upper and lower bound concept?

I am having trouble with how to set up the synthetic division. Like what numbers I use.

Originally Posted by tsmith

Like what numbers I use.

You use 3 and -4. Because this is what you are given. So,

3 | 2 +0 +0 -8 +3
____+6+18+54+138__
__ _2 6 18 46 141

Now, from the upper and lower bound rule, you can confirm that 3 is an upper bound because all of the numbers in thel ast row (6,18,46,141) are all positive.

Does this help you?

This is extremely helpful. So now I do the synthetic division for -4, right?

Originally Posted by tsmith

This is extremely helpful. So now I do the synthetic division for -4, right?

Right, but remember that the rule for the lower bound is different.

I completely understand. Thank you so much for your help.

Originally Posted by tsmith

I completely understand. Thank you so much for your help.