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CBSE Class 11-science Answered

If range of values of a for which roots of the equation x^2-2x-a^2-1=0 lie between the roots of x^2-2(a+1)x+a(a-1)=0 is p,q then find the value of q-1/p. 
Asked by aahnik.mohanty | 21 Jun, 2019, 09:04: PM
answered-by-expert Expert Answer
x squared minus 2 x minus open parentheses a squared minus 1 close parentheses equals 0 R o o t s space o f space t h e space a b o v e space e q u a t i o n space a r e x equals fraction numerator 2 plus-or-minus square root of 4 plus 4 open parentheses a squared minus 1 close parentheses end root over denominator 2 end fraction space space equals fraction numerator 2 plus-or-minus square root of 4 plus 4 a squared minus 4 end root over denominator 2 end fraction space space equals fraction numerator 2 plus-or-minus 2 a over denominator 2 end fraction space space equals space 1 plus a comma space 1 minus a N o w comma space t h e r e space a r e space t h r e e space c o n d i t i o n s 1 minus a equals 0 space space o r space 1 minus a less than 0 space space space o r space 1 minus a greater than 0 T h e space s e c o n d space e q space i s space x squared minus 2 left parenthesis a plus 1 right parenthesis x plus a left parenthesis a minus 1 right parenthesis R o o t s space a r e colon x equals fraction numerator 2 left parenthesis a plus 1 right parenthesis plus-or-minus square root of 4 left parenthesis a plus 1 right parenthesis squared minus 4 a open parentheses a minus 1 close parentheses end root over denominator 2 end fraction space space equals fraction numerator 2 left parenthesis a plus 1 right parenthesis plus-or-minus square root of 4 a squared plus 8 a plus 4 minus 4 a squared plus 4 a end root over denominator 2 end fraction space space equals fraction numerator 2 left parenthesis a plus 1 right parenthesis plus-or-minus square root of 12 a plus 4 end root over denominator 2 end fraction space space equals left parenthesis a plus 1 right parenthesis plus-or-minus square root of 3 a plus 1 end root T h e r e space a r e space 3 space c o n d i t i o n s left parenthesis a plus 1 right parenthesis plus-or-minus square root of 3 a plus 1 end root equals 0 space space o r space space space left parenthesis a plus 1 right parenthesis plus-or-minus square root of 3 a plus 1 end root greater than 0 space space o r space space space space left parenthesis a plus 1 right parenthesis plus-or-minus square root of 3 a plus 1 end root less than 0 rightwards double arrow a equals 0 space o r space 1 W h e n space a equals 0 comma t h e space r o o t s space o f space f i r s t space e q space i s space 1 comma space w h i c h space l i e s space b e t w e e n space 0 space a n d space 2 W h e n space a equals 1 comma space r o o t s space o f space f i r s t space e q space a r e space 0 space a n d space 2 w h i c h space l i e s space b e t w e e n space 0 space a n d space 2 H e n c e comma space fraction numerator q minus 1 over denominator p end fraction equals fraction numerator 0 minus 1 over denominator 2 end fraction equals negative 1 half space w h e n space p equals 2 space a n d space q equals 0 A l s o comma space fraction numerator q minus 1 over denominator p end fraction equals fraction numerator 2 minus 1 over denominator 0 end fraction space equals infinity space w h e n space p equals 0 space a n d space q equals 2
Answered by Renu Varma | 25 Jun, 2019, 10:55: AM

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