a-b-c-are-given-real-constants-p-q-r-t-are-unknowns-from-which-we-can-choose-values-of-two-of-them-non-zero-and-have-to-determine-the-other-two-non-zero-obeying-two-equations-given-below-p-2-

Question Number 74412 by ajfour last updated on 24/Nov/19

a, b, c a r e g i v e n r e a l c o n s t a n t s .

p, q, r, t a r e u n k n o w n s f r o m w h i c h

w e c a n c h o o s e v a l u e s o f t w o o f

t h e m (n o n z e r o) a n d h a v e t o

d e t e r m i n e t h e o t h e r t w o (n o n z e r o),

o b e y i n g t w o e q u a t i o n s g i v e n b e l o w

p^{2} + q (1 + b q) t^{2} + q (a p + b r) t

+ r (1 + b q) t + r (a p + b r) = 0

p t + q (a + c q) t^{2} + r (a + c q) t

+ c q r t + {c r}^{2} = 0

C a n t h i s b e d o n e s o l v i n g a

q u a d r a t i c e q . a n d n o n e h i g h e r . . ?