The expression is .

(a)

Intermediate value theorem :

The function  is continuous on the closed interval , let  be the number between  and , where  then exist a number  in  such that .

Consider the function is .

Consider the function  to be continuous over the interval .

Prove that the number  exists between  and .

.

Substitute  in the above function.

Substitute  in the above function.

Thus, .

Then according to intermediate value theorem, there exist at least one root between  and  such that . 

(b)

Graph :

Graph the function  :

Observe the graph.

.

Therefore the root of the function is .

The root of the function is .