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Sir plz solve it with full explanation

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Asked by vishakhachandan026 14th June 2019, 11:09 AM
Answered by Expert
Answer:
x squared minus 4 vertical line x vertical line plus 3 minus vertical line k minus 1 vertical line equals 0
rightwards double arrow vertical line x vertical line squared minus 4 vertical line x vertical line plus 3 minus vertical line k minus 1 vertical line equals 0 space space h a s space f o u r space r e a l space r o o t s
T h e r e f o r e comma space d i s c r i m i n i n a n t space D greater than 0
rightwards double arrow b squared minus 4 a c greater than 0
rightwards double arrow left parenthesis negative 4 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 3 minus vertical line k minus 1 vertical line right parenthesis greater than 0
rightwards double arrow 16 minus 12 plus 4 vertical line k minus 1 vertical line greater than 0
rightwards double arrow 4 plus 4 vertical line k minus 1 vertical line greater than 0
rightwards double arrow 4 vertical line k minus 1 vertical line greater than negative 4
rightwards double arrow vertical line k minus 1 vertical line greater than negative 1
w h i c h space i s space t r u e space f o r space a l l space k element of R
N o w comma space t h e space s e c o n d space c o n d i t i o n space i s colon
F o r space r o o t s space t o space b e space p o s i t i v e comma
left parenthesis i right parenthesis space s u m space o f space t h e space r o o t s equals negative b over a space greater than 0
left parenthesis i i right parenthesis space p r o d u c t space o f space t h e space r o o t s equals c over a space greater than 0
rightwards double arrow space left parenthesis i right parenthesis space 4 greater than 0
w h i c h space i s space t r u e space a l w a y s
left parenthesis i i right parenthesis c over a space greater than 0
rightwards double arrow 3 minus vertical line k minus 1 vertical line greater than 0
rightwards double arrow 3 greater than vertical line k minus 1 vertical line
rightwards double arrow vertical line k minus 1 vertical line less than 3
rightwards double arrow negative 3 less than k minus 1 less than 3
rightwards double arrow negative 2 less than k less than 4
H e n c e comma space k element of left parenthesis negative 2 comma 4 right parenthesis
Answered by Expert 17th June 2019, 10:32 AM
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