Asked by Sanmit Ratnaparkhi | 29th Oct, 2014, 02:27: PM

Expert Answer:

4. 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 space i s space a x squared plus b x plus c equals 0 S u m space o f space t h e space r o o t s space equals minus b over a P r o d u c t space o f space t h e space r o o t s equals c over a S i n c e space s u m space o f space t h e space r o o t s space i s space e q u a l space t o space t h e space P r o d u c t space o f space t h e space r o o t s comma space w e space h a v e comma minus b over a equals c over a rightwards double arrow minus b equals c rightwards double arrow b plus c equals 0 H e n c e space t h e space c o r r e c t space o p t i o n space i s space left parenthesis 3 right parenthesis  5. space G i v e n space r o o t s space a r e space p space a n d space 1 over p ; S u m space o f space t h e space r o o t s equals p plus 1 over p equals fraction numerator p squared plus 1 over denominator p end fraction ; P r o d u c t space o f space t h e space r o o t s equals p cross times 1 over p equals 1 T h u s comma space t h e space q u a d r a t i c space e q u a t i o n space i s space x squared minus s u m space o f space t h e space r o o t s cross times x plus p r o d u c t space o f space t h e space r o o t s equals 0 T h a t space i s comma space t h e space e q u a t i o n space i s space x squared minus fraction numerator p squared plus 1 over denominator p end fraction cross times x plus 1 equals 0 rightwards double arrow space p x squared minus open parentheses p squared plus 1 close parentheses x plus p equals 0 H e n c e space t h e space c o r r e c t space o p t i o n space i s space left parenthesis 2 right parenthesis.  11. 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 space i s space x squared plus k open parentheses 4 x plus k minus 1 close parentheses plus 2 equals 0 G i v e n space t h a t space t h e space 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 space r e a l space a n d space e q u a l. H e n c e space t h e space v a l u e space o f space t h e space d i s c r i m i n a n t space i s space z e r o. T h a t space i s space D equals b squared minus 4 a c equals o R e w r i t i n g space t h e space g i v e n space q u a d r a t i c space a s space f o l l o w s : x squared plus 4 k x plus k squared minus k plus 2 equals 0 T h u s comma space b equals 4 k comma space a equals 1 space a n d space c equals k squared minus k plus 2 T h u s comma space D equals 16 k squared minus 4 open parentheses k squared minus k plus 2 close parentheses equals 0 rightwards double arrow 16 k squared minus 4 k squared plus 4 k minus 8 equals 0 rightwards double arrow 12 k squared plus 4 k minus 8 equals 0 rightwards double arrow 3 k squared plus k minus 2 equals 0 rightwards double arrow 3 k squared plus 3 k minus 2 k minus 2 equals 0 rightwards double arrow 3 k open parentheses k plus 1 close parentheses minus 2 open parentheses k plus 1 close parentheses equals 0 rightwards double arrow open parentheses 3 k minus 2 close parentheses open parentheses k plus 1 close parentheses equals 0 rightwards double arrow k equals 2 over 3 comma space k equals minus 1 H e n c e space t h e space c o r r e c t space o p t i o n space i s space left parenthesis 4 right parenthesis.
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Answered by Vimala Ramamurthy | 30th Oct, 2014, 10:08: AM