CBSE Class 10 Answered

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

Asked by P S Lakshmi | 09 Mar, 2015, 11:00: PM

Expert Answer

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

Answered by Prasenjit Paul | 10 Mar, 2015, 04:01: PM

CBSE Class 10 Answered

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CBSE Class 10 Answered

Application Videos

Nature of Roots

Determining roots and nature of roots using discriminan ...

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Concept Videos

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Nature of Roots

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D = 0

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