Given-that-the-equation-3x-2-mx-n-0-has-roots-1-and-1-find-the-value-of-m-and-n-

Question Number 49118 by Rio Michael last updated on 03/Dec/18

G i v e n t h a t t h e e q u a t i o n 3 x^{2} + m x + n = 0 h a s r o o t s α + \frac{1}{β} a n d

β + \frac{1}{α} f i n d t h e v a l u e o f m a n d n

Answered by Kunal12588 last updated on 03/Dec/18

3 x^{2} + m x + n = 0

α + \frac{1}{β} + β + \frac{1}{α} = - \frac{m}{3}

\frac{α^{2} β + α + α β^{2} + β}{α β} = - \frac{m}{3}

m = - 3 \frac{(α + β) (1 + α β)}{α β}

(α + \frac{1}{β}) (β + \frac{1}{α}) = \frac{n}{3}

α β + 1 + 1 + \frac{1}{α β} = \frac{n}{3}

n = 3 \frac{α^{2} β^{2} + 2 α β + 1}{α β}

n = \frac{3 {(α β + 1)}^{2}}{α β}