Bounds on zeros :

Let denote a polynomial function whose leading coefficient is .

A bound on the real zeros of is the smaller of the two numbers.

.

Where means " choose the largest entry in ".

The polynomial function is .

First write so that it is the product of a constant times a polynomial whose leading coefficient is by factoring out the leading coefficient of ,.

Evaluate the two expressions .

Consider .

Compare the above polynomial with .

, and .

The smaller of the two numbers, , is the bound.

Every real zero of lies between and .

The Theorem on Bounds of Zeros tells that every zero is between and .

Draw a coordinate plane.

Graph the polynomial function using .

Observe the above graph :

The function has exactly one positive - intercept at .

Thus, the positive real zero is .

The positive real zero is .