Given that the equation 3x^2 +mx+n=0 has roots α + (1/β) and β + (1/(α )) find the value of m and n


Question and Answers Forum

All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
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

	$3 x^{2} + m x + n = 0$ $α + \frac{1}{β} + β + \frac{1}{α} = - \frac{m}{3}$ $\frac{α^{2} β + α + α β^{2} + β}{α β} = - \frac{m}{3}$ $m = - 3 \frac{(α + β) (1 + α β)}{α β}$ $(α + \frac{1}{β}) (β + \frac{1}{α}) = \frac{n}{3}$ $α β + 1 + 1 + \frac{1}{α β} = \frac{n}{3}$ $n = 3 \frac{α^{2} β^{2} + 2 α β + 1}{α β}$ $n = \frac{3 {(α β + 1)}^{2}}{α β}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum