question is :

Dear Student,

It does depend whether either 'a' or 'b' is also one of the root.

If neither of them is a root,

then the interval can contain atmost k roots of p'(x) = 0;

You can judge it from the diagram below:

The circle represents the real roots of p(x) and the horizontal lines represent the real roots of p'(x) =0;

both are equal to 4.

 

Regards,