Yes, exactly that.
I was just using ##q(x)## as the quotient polynomial ##(a_{n-1} x^{n-1} + a_{n-2} x^{n-2} + \cdots + a_1 x + a_0)##, and ##r## as the remainder as the book does.
I actually found a preview online of the exact two pages from the book which would make it clearer: Theorem 3.11.
OK, thanks for looking, I will try to be a bit clearer:
Suppose ##f## is a polynomial of degree ##n ≥ 1##
If ##c > 0## is synthetically divided into ##f## and all of the numbers in the final line of the division tableau have the same signs, then ##c## is an upper bound for the real zeros...
Homework Statement
Upper Bound[/B]
If all of the numbers in the final line of the synthetic division tableau are non-positive, prove for ##f(b)<0##, no real number ##b > c## can be a zero of ##f##
Lower Bound
To prove the lower bound part of the theorem, note that a lower bound for the...
Thanks so much for your help Stephen I think that clears it up. I think it's a case of a book giving particular definitions of the notation and convention to get past a certain point with the assumed knowledge of that level which is "good enough" until such times a deeper explanation can be...
Thanks Stephen for your reply.
I think I have a better idea now.
If I understand correctly, what needs to happen is that the fractional exponent needs to be expressed or understood in simplest terms first. The exponent should never be a ratio of two even numbers because a factor of 2 can...
Homework Statement
I'm trying to understand negative bases raised to rational powers, when calculating principle roots for real numbers. I'm not worried about complex solutions numbers at this stage. I just can't find a concise explanation I can understand anywhere. I'm self learning as an...