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give answer of both paragraphs

Asked by rbhatt16 12th October 2017, 5:10 PM
Answered by Expert
Answer:
Let us find the condition for one root < 2 and other root >2
 
begin mathsize 12px style x squared minus left parenthesis m minus 3 right parenthesis x space plus space m space equals space 0

r o o t s space a r e space fraction numerator left parenthesis m minus 3 right parenthesis plus-or-minus square root of open parentheses m minus 3 close parentheses squared minus 4 m end root over denominator 2 end fraction space semicolon space t h i s space c a n space b e space w r i t t e n space a s space space fraction numerator left parenthesis m minus 3 right parenthesis plus-or-minus square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root over denominator 2 end fraction

L e t space t h e space s m a l l e r space r o o t space space fraction numerator left parenthesis m minus 3 right parenthesis minus square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root over denominator 2 end fraction space less than 2

left parenthesis m minus 3 right parenthesis minus square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root space less than space 4 space space

left parenthesis m minus 7 right parenthesis space less than space square root of open parentheses m minus 1 close parentheses left parenthesis m minus 9 right parenthesis end root
m squared minus 14 m plus 49 space less than space m squared minus 10 m plus 9
t h i s space g i v e s space t h e space c o n d i t i o n space space m space greater than space 10
end style
begin mathsize 12px style L e t space t h e space b i g g e r space r o o t space fraction numerator left parenthesis m minus 3 right parenthesis plus square root of open parentheses m minus 3 close parentheses squared minus 4 m end root over denominator 2 end fraction space space greater than space 2
h e n c e space space square root of open parentheses m minus 1 close parentheses open parentheses m minus 9 close parentheses end root space greater than space left parenthesis 7 minus m right parenthesis space left parenthesis p l e a s e space w o r k o u t space t h e space a l g e b r a space a s space d o n e space i n space p r e v i o u s space c a s e right parenthesis

h e n c e space m squared minus 10 m plus 9 space greater than space m squared minus 14 m plus 49 space a n d space t h i s space l e a d s space t o space m space greater than 10

end style
So the answer is m lies between 10 and ∞   (10, ∞ )
 
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for both roots >2
 
if we work out same way as above for smaller root we get m<10 and for bigger root m>10
 
but we need begin mathsize 12px style square root of left parenthesis m minus 3 right parenthesis squared minus 4 m end root end style should be positive and this leads the condition m > 9.
Hence the answer is m lies between 9 and 10 , (9,10)
 
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if you work out same way, for one root > 1 and other root <2 again the answer is (9,10)
 
 
The question related to second paragraph is not answered because for one post only one question is allowed

Answered by Expert 18th October 2017, 12:32 PM
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