Find the relation between p q and r if one of the root of the equation px^2 +qx+r=0 is double the other.


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Question Number 52573 by Necxx last updated on 09/Jan/19

$F i n d t h e r e l a t i o n b e t w e e n p q a n d r$ $i f o n e o f t h e r o o t o f t h e e q u a t i o n$ ${p x}^{2} + q x + r = 0 i s d o u b l e t h e o t h e r .$
	Answered by mr W last updated on 09/Jan/19

	${p x}^{2} + q x + r = p (x - a) (x - 2 a)$ ${p x}^{2} + q x + r = p (x^{2} - 3 a x + 2 a^{2})$ $\Rightarrow q = - 3 p a$ $\Rightarrow r = 2 {p a}^{2}$ $\Rightarrow r = 2 p {(- \frac{q}{3 p})}^{2} = \frac{2 q^{2}}{9 p}$ $\Rightarrow 9 p r = 2 q^{2}$
	Commented by Necxx last updated on 10/Jan/19

	$t h a n k y o u s i r$
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