The roots of the equation 2x^2 +px+q=0 are 2α+β and α+2β. Calculate the values of p and q


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Question Number 158829 by MathsFan last updated on 09/Nov/21

$T h e r o o t s o f t h e e q u a t i o n$ $2 x^{2} + p x + q = 0 a r e 2 α + β a n d$ $α + 2 β . C a l c u l a t e t h e v a l u e s o f$ $p a n d q$
Commented by Rasheed.Sindhi last updated on 09/Nov/21

$N u m e r i c a l a n s w e r s o f p & q a r e n o t$ $p o s s i b l e b e c a u s e d a t a i s i n s u f f i c i e n t .$
Commented by MathsFan last updated on 09/Nov/21

$yeah, sure$
	Answered by ajfour last updated on 09/Nov/21

	$(2 α + β) + (α + 2 β) = 3 (α + β) = - \frac{p}{2}$ $(2 α + β) (α + 2 β)$ $= 2 {(α + β)}^{2} + α β = \frac{q}{2}$ $\Rightarrow \frac{p^{2}}{18} + α β = \frac{q}{2}$ $p = - 6 (α + β); q = \frac{p^{2}}{9} + 2 α β$
	Commented by MathsFan last updated on 09/Nov/21

	$thank you$
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