let us define a function , which is the function of and

at where

is zero and also at ,
There are about zero’s at
If we impose the law of mean value on , then must be continuous and differentiable. Also there exists a root of between each of the zeros of that is there and a total of zeros of . If there exists then there are zeros and similarly if the derivative exists then there exist at least a zero in the interval of
let us call this as