Question

 Show that the equation x3 - 15x + c = 0 has at most one root in the interval [-2, 2].

Answer 1

Step 1:

The equation is and the interval .

Consider .

The function is  is continuous on the closed interval .

Consider then ,

Consider then ,

It follows that and .

Therefore apply the intermediate theorem to state that there must be some k in Such that f (k)=c .

has atmost one zero in the closed interval .

Solution:

has atmost one zero in the closed interval .