Dear Sir/Madam
 
This question actually comes under pure algebra and is not exactly from this chapter.
 
If a and b are roots of y^2-4y+1=0 and c and d are roots of y^2+7y+1=0, find (a-b)(b-c)(a-d)(b-d).
 
Regards
Navya

Asked by Navya Benny | 16th Jun, 2015, 08:37: PM

Expert Answer:

T h e space e x p r e s s i o n space i n space t h e space q u e s t i o n space s e e m s space i n c o r r e c t. space A f t e r space m a k i n g space t h e space e x p r e s s i o n space open parentheses a minus c close parentheses open parentheses b minus c close parentheses open parentheses a minus d close parentheses open parentheses b minus d close parentheses comma space w e space p r o c e e d space a s space f o l l o w s colon y squared minus 4 y plus 1 equals 0 space h a s space r o o t s space a space a n d space b H e n c e comma space a plus b equals 4 comma space a b equals 1 a squared minus 4 a plus 1 equals 0 rightwards double arrow a squared equals 4 a minus 1.. left parenthesis 1 right parenthesis S i m i l a r l y comma space b squared equals 4 b minus 1... left parenthesis 2 right parenthesis y squared plus 7 y plus 1 equals 0 space h a s space r o o t s space c space a n d space d H e n c e comma space c plus d equals negative 7 comma space c d equals 1
N o w comma space space open parentheses a minus c close parentheses open parentheses b minus c close parentheses open parentheses a minus d close parentheses open parentheses b minus d close parentheses equals open square brackets space open parentheses a minus c close parentheses open parentheses a minus d close parentheses close square brackets open square brackets open parentheses b minus c close parentheses open parentheses b minus d close parentheses close square brackets equals open square brackets a squared minus open parentheses c plus d close parentheses a plus c d close square brackets open square brackets b squared minus open parentheses c plus d close parentheses b plus c d close square brackets equals open square brackets a squared plus 7 a plus 1 close square brackets open square brackets b squared plus 7 b plus 1 close square brackets U sin g space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space g e t space open parentheses a minus c close parentheses open parentheses b minus c close parentheses open parentheses a minus d close parentheses open parentheses b minus d close parentheses equals open square brackets 4 a minus 1 plus 7 a plus 1 close square brackets open square brackets 4 b minus 1 plus 7 b plus 1 close square brackets equals 11 a cross times 11 b equals 11 a b equals 11 cross times 1 equals 11

Answered by satyajit samal | 18th Jun, 2015, 10:02: AM

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