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Home / Doubts and Solutions/ICSE/Class 11 Science/Mathematics

find the values of p if the roots of the equation (p-3)x^2-2px+5p=0 are positive.

Asked by renuy307 4th June 2019, 1:42 PM
Answered by Expert
Answer:
L e t space a space a n d space b space b e space t h e space space r o o t s space o f space t h e space e q u a t i o n space left parenthesis p minus 3 right parenthesis x squared minus 2 p x plus 5 p equals 0 S i n c e space i t space i s space g i v e n space t h a t space t h e space r o o t s space o f space a b o v e space e q u a t i o n space a r e space p o s i t i v e rightwards double arrow a comma space b greater than 0 rightwards double arrow a plus b greater than 0 space a n d space a b greater than 0 rightwards double arrow fraction numerator 2 p over denominator p minus 3 end fraction greater than 0 space a n d space fraction numerator 5 p over denominator p minus 3 end fraction greater than 0 S i n c e comma space fraction numerator 2 p over denominator p minus 3 end fraction greater than 0 rightwards double arrow 2 p greater than 0 space a n d space p minus 3 greater than 0 space O R space 2 p less than 0 space a n d space p minus 3 less than 0 rightwards double arrow p greater than 0 space a n d space p greater than 3 space O R space p less than 0 space a n d space p less than 3 rightwards double arrow p element of left parenthesis 3 comma infinity right parenthesis space O R space p element of left parenthesis 3 comma infinity right parenthesis rightwards double arrow p element of left parenthesis negative infinity comma 0 right parenthesis union left parenthesis 3 comma infinity right parenthesis A l s o comma space fraction numerator 5 p over denominator p minus 3 end fraction greater than 0 rightwards double arrow 5 p greater than 0 space a n d space p minus 3 greater than 0 space O R space 5 p less than 0 space a n d space p minus 3 less than 0 rightwards double arrow p greater than 0 space a n d space p greater than 3 space O R space p less than 0 space a n d space p less than 3 rightwards double arrow p element of left parenthesis 3 comma infinity right parenthesis space O R space p element of left parenthesis 3 comma infinity right parenthesis rightwards double arrow p element of left parenthesis negative infinity comma 0 right parenthesis union left parenthesis 3 comma infinity right parenthesis H e n c e comma space t h e space a n s w e r space i s space p element of left parenthesis negative infinity comma 0 right parenthesis union left parenthesis 3 comma infinity right parenthesis.
Answered by Expert 4th June 2019, 4:10 PM
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