2.If the difference of roots of the quadratic equation x^2+4px+p=0 is same as the difference of roots of quadratic equation x^2+4px+q=0,then find the relation between p and q if p!=q. 3.if x^2+5x+6+k=0,then the value of for which roots of the given equation differ by 1 is

Asked by nitinkumarsingh.singh.75 | 29th Jul, 2015, 01:02: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n s x squared plus 4 p x plus p equals 0... left parenthesis 1 right parenthesis a n d x squared plus 4 q x plus q equals 0... left parenthesis 2 right parenthesis G i v e n space t h a t space t h e space d i f f e r e n c e space o f space r o o t s space o f space t h e space g i v e n space q u a d r a t i c space e q u a t i o n s space a r e space s a m e. L e t space a space a n d space b space a r e space t h e space r o o t s space o f space e q u a t i o n space left parenthesis 1 right parenthesis space a n d space c space a n d space d space a r e space t h e space r o o t s space o f space e q u a t i o n space left parenthesis 2 right parenthesis rightwards double arrow a minus b equals c minus d... left parenthesis 3 right parenthesis a plus b equals negative 4 p space a n d space c plus d equals negative 4 q a b equals p space a n d space c d equals q S q u a r i n g space b o t h space t h e space s i d e s space o f space t h e space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma open parentheses a minus b close parentheses squared equals open parentheses c minus d close parentheses squared... left parenthesis 4 right parenthesis W e space k n o w space t h a t open parentheses a minus b close parentheses squared equals open parentheses a plus b close parentheses squared minus 4 a b a n d open parentheses c minus d close parentheses squared equals open parentheses c plus d close parentheses squared minus 4 c d therefore E q u a t i o n space left parenthesis 4 right parenthesis space b e c o m e s open parentheses a plus b close parentheses squared minus 4 a b equals open parentheses c plus d close parentheses squared minus 4 c d rightwards double arrow open parentheses negative 4 p close parentheses squared minus 4 p equals open parentheses negative 4 q close parentheses squared minus 4 q rightwards double arrow 16 p squared minus 4 p equals 16 q squared minus 4 q rightwards double arrow 4 p squared minus 4 q squared equals p minus q rightwards double arrow 4 open parentheses p minus q close parentheses open parentheses p plus q close parentheses equals p minus q rightwards double arrow 4 open parentheses p plus q close parentheses equals 1 rightwards double arrow open parentheses p plus q close parentheses equals 1 fourth
Kindly post one question per query.

Answered by Vimala Ramamurthy | 30th Jul, 2015, 10:51: AM

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