P-x-x-n-a-n-1-x-n-1-a-1-x-a-0-be-a-polynomial-with-all-the-real-roots-prove-that-n-1-a-n-1-2-2na-n-2-

Question Number 33834 by uddipan last updated on 25/Apr/18

P (x) = x^{n} + a_{n - 1} x^{n - 1} + \dots . a_{1} x + a_{0} b e a p o l y n o m i a l w i t h a l l t h e r e a l r o o t s,

p r o v e t h a t (n - 1) a_{n - 1}^{2} ⩾ 2 {n a}_{n - 2} .