Question
Mon March 09, 2015 By: P S Lakshmi

If (a.a + b.b)x.x - 2(ac+bd)x + (c.c + d.d) , has equal roots, show that  ad=bc

Expert Reply
Prasenjit Paul
Tue March 10, 2015
open parentheses a squared plus b squared close parentheses x squared minus 2 open parentheses a c plus b d close parentheses x plus open parentheses c squared plus d squared close parentheses equals 0 S i n c e space t h e space r o o t s space a r e space e q u a l comma space d i s c r i m i n a n t space s h o u l d space b e space e q u a l space t o space z e r o. open parentheses 2 open parentheses a c plus b d close parentheses close parentheses squared minus 4 open parentheses a squared plus b squared close parentheses open parentheses c squared plus d squared close parentheses equals 0 rightwards double arrow 4 open parentheses a squared c squared plus b squared d squared plus 2 a b c d close parentheses minus 4 open parentheses a squared c squared plus a squared d squared plus b squared c squared plus b squared d squared close parentheses equals 0 rightwards double arrow open parentheses a squared c squared plus b squared d squared plus 2 a b c d close parentheses minus open parentheses a squared c squared plus a squared d squared plus b squared c squared plus b squared d squared close parentheses equals 0 rightwards double arrow a squared c squared plus b squared d squared plus 2 a b c d minus a squared c squared minus a squared d squared minus b squared c squared minus b squared d squared equals 0 rightwards double arrow a squared c squared plus b squared d squared plus 2 a b c d minus a squared c squared minus a squared d squared minus b squared c squared minus b squared d squared equals 0 rightwards double arrow 2 a b c d minus a squared d squared minus b squared c squared equals 0 rightwards double arrow left parenthesis a d right parenthesis squared plus left parenthesis b c right parenthesis squared minus 2 left parenthesis a d right parenthesis left parenthesis b c right parenthesis equals 0 rightwards double arrow left parenthesis a d minus b c right parenthesis squared equals 0 rightwards double arrow left parenthesis a d minus b c right parenthesis equals 0 therefore a d equals b c H e n c e space P r o v e d
Home Work Help