roll theorem prove question..

question :

suppose that to the quadratic equation x^2+px+q=0

has two roots

prove that for

there are n different roots on the interval (x1,x2)

??

the prove:

by rolls theorem we have a point "c" on the interval of (x1,x2) for which

f'(c)=0

then they say

"that we can get another solution "g" on the interval of (x1,c) using rolls theorem"

but its not rolls theorem

we dont have two points for which there is a point "j" for which f'(j)=0

we have f(x1)=0 and f'(c)=0 (but its not f(c)=0 )

??