# Interval of Polynomial Root Finding

Let's say we have a polynomial of a given degree. You don't have any tools to figure out the amount of roots in this polynomial. All you know is the function and you cannot graph it. How would you find the interval of which all the roots of the polynomial lie?

I have this so far: $ax^n + bx^{n - 1} + \dots + \Omega = 0$

$ax^n = -bx^{n - 1} - \dots - \Omega$

But how do I continue from here?

• There are a lot of different bounds which might be useful, see here for a start. – Antonio Vargas Apr 24 '15 at 3:27