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 .

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 between .

The equation is .

The interval is .

Therefore the solution is in the interval .

Divide the interval into equal subintervals :

Now find the value of at each end point until the intermediate value theorem applies.

Stop here and conclude that the value of  zero is in between and .

Divide the interval into equal subintervals and proceed to evaluate at each end point.

Stop here and conclude that zero lies between and and correct to two decimal places the zero is .

The value of is .