Question

Use Rolle's Theorem to prove that between every two zeros of \(x^n + a_{n-1}x^{n-1}+...+a_1x+a_0\) there lies a zero of \(nx^{n-1}+(n-1)a_{n-1}x^{x-2}+...+a_1\).

Answer 1

note that the second polynomial is the derivative of original one

Answer 2

wiki

If a real-valued function ƒ is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and ƒ(a) = ƒ(b), then there exists a c in the open interval (a, b) such that\[f'(c)=0\]

Answer 3

for every 2 zeroes of original polynomial like a<b apply rolles theorem

Answer 4

thats quite right :)

Answer 5

That means something's wrong?!

Answer 6

i mean thats correct :)

Answer 7

Oh.. Sorry!! and thanks too!!!!!

Answer 8

no problem