i f space f open parentheses x close parentheses equals open parentheses x minus a close parentheses open parentheses x minus c close parentheses plus 2 open parentheses x minus b close parentheses open parentheses x minus d close parentheses a n d space a l s o space a less than b less than c less than d f i n d space t h e space n a t u r e space o f space r o o t s
 
 science:
Q1. in a room it is best to place a room heater on the floor but an air conditioner near the ceiling. why?
 

Asked by badesraajay | 3rd Aug, 2015, 07:54: PM

Expert Answer:

G i v e n space f open parentheses x close parentheses equals open parentheses x minus a close parentheses open parentheses x minus c close parentheses plus 2 open parentheses x minus b close parentheses open parentheses x minus d close parentheses comma space a less than b less than c less than d rightwards double arrow f open parentheses x close parentheses equals x squared minus open parentheses a plus c close parentheses x plus a c plus 2 open square brackets x squared minus open parentheses b plus d close parentheses x plus b d close square brackets rightwards double arrow f open parentheses x close parentheses equals x squared minus open parentheses a plus c close parentheses x plus a c plus 2 x squared minus 2 open parentheses b plus d close parentheses x plus 2 b d rightwards double arrow f open parentheses x close parentheses equals 3 x squared minus open parentheses a plus 2 b plus c plus 2 d close parentheses x plus a c plus 2 b d H e r e comma space A equals 3 comma space B equals negative open parentheses a plus 2 b plus c plus 2 d close parentheses space a n d space C equals a c plus 2 b d T h e r e f o r e comma space t h e space d i s c r i m i n a n t space o f space t h e space a b o v e space e q u a t i o n space i s triangle equals B squared minus 4 A C space space space space space equals open parentheses a plus 2 b plus c plus 2 d close parentheses squared minus 4 cross times 3 cross times open parentheses a c plus 2 b d close parentheses space space space space space equals open parentheses a plus 2 b plus c plus 2 d close parentheses squared minus 12 open parentheses a c plus 2 b d close parentheses space space space space space equals open square brackets open parentheses a plus 2 d close parentheses minus open parentheses c plus 2 b close parentheses close square brackets squared plus 4 open parentheses a plus 2 d close parentheses open parentheses c plus 2 b close parentheses minus 12 open parentheses a c plus 2 b d close parentheses space space space space space equals open square brackets open parentheses a plus 2 d close parentheses minus open parentheses c plus 2 b close parentheses close square brackets squared plus 8 a b plus 8 c d minus 8 a c minus 8 b d space space space space space equals open square brackets open parentheses a plus 2 d close parentheses minus open parentheses c plus 2 b close parentheses close square brackets squared plus 8 open parentheses c minus b close parentheses open parentheses d minus a close parentheses S i n c e space a less than d space a n d space b less than c comma space t h e space p r o d u c t space 8 open parentheses c minus b close parentheses open parentheses d minus a close parentheses space i s space a l w a y s space p o s i t i v e. T h u s comma space 8 open parentheses c minus b close parentheses open parentheses d minus a close parentheses greater than 0 S i n c e space s q u a r e space t e r m space i s space a l w a y s space p o s i t i v e comma space w e space h a v e comma space open square brackets open parentheses a plus 2 d close parentheses minus open parentheses c plus 2 b close parentheses close square brackets squared greater than 0 T h e r e f o r e comma space t h e space d i s c r i m i n a n t space triangle greater than 0 H e n c e space t h e space r o o t s space a r e space r e a l space a n d space u n i q u e.

Answered by Vimala Ramamurthy | 4th Aug, 2015, 11:31: AM