The-roots-of-the-equation-2x-2-px-q-0-are-2-and-2-Calculate-the-values-of-p-and-q-

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