I have a question if someone has a few minutes to explain it to me.
I am going over my practice test and one of the questions if the thread title. I am unsure if I understand what it is asking. Does it want what the bounds are that the real zeros will be in?
The function is x^5+2x^4+2x^3-7x^2+x+4
According to the test, the answer is -8 and 8 but I have no idea how to get there. Looking at the graph of the function, I would think it would fall between -1 and 1, but again, I am unsure as to what it is asking for when asking for the bounds.
Our instructor missed class the other day so we have not went over this and I am trying to stay ahead.
This is what I have in my textbook about bounds. A positive number M is a bound on the zeros of a polynomial if every zero r lies between -M and M, inclusive. That is, M is a bound to the zeros of a polynomial f is -M less than/equal to any zero of f less than/equal to M.
In looking at the textbook, I think I need to take the leading coefficient which is 1 and add it to the absolute value of -7 which is 7 and that is 8. Or I add the absolute value of all the coefficients and take which ever is the lesser number?
Could someone please explain to me or show me how the answer is -8 and 8?
Like I said, my instructor missed class last week and while we will still cover what we missed that day, I am sure she will rush through it since this is an accelerated summer course. I am simply trying to make some sense of what we will cover in class before we cover it.
Have you looked at the links I provided? Cauchy bound is exactly 8 for this polynomial.