if the roots of the equation

Asked by renukasahu8 | 19th Oct, 2010, 09:23: PM

Expert Answer:

Dear Student,
If the roots are equal then the discriminant must be zero.
(-2(ac+bd))2 - 4(a2+b2)(c2+d2) = 0
4(ac+bd)2 - 4(a2+b2)(c2+d2) = 0
(ac+bd)2 = (a2+b2)(c2+d2
a2c2 + 2abcd + b2d2 = a2c2 + a2d2 + b2c2 + b2d2 
2abcd  =  a2d2 + b2c2  
a2d2 - 2abcd + b2c2 = 0   
(ad - bc)2 = 0
ad - bc = 0
ad = bc
a/b = c/d
Hence proved.
regards,
Team,
TopperLearning.

Answered by  | 19th Oct, 2010, 09:37: PM

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