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


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

$P (x) = x^{n} + a_{n - 1} x^{n - 1} + . . . . a_{1} x + a_{0} b e a p o l y n o m i a l w i t h a l l t h e r e a l r o o t s,$ $p r o v e t h a t (n - 1) a_{n - 1}^{2} ⩾ 2 {n a}_{n - 2} .$
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