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CBSE Class 11-science Answered

Proving type
Asked by | 14 May, 2012, 08:44: PM
answered-by-expert Expert Answer
the equation in quadratic can be written as 
a(x+2)4 + b(x+2)2 + c = 0
 
Let (x+2)2 = t , So the equation becomes
 
at2 + bt + c = 0 
 
Now since b2 - 4ac > 0 , thus D > 0
 
Now t = {-b +- root(D) }/2a
 
Also t = (x+2)2 , thus t cannot be negative ,
 
Now ,
CASE 1 :
If b>0 , then b must be greater than both a , c , also a and c must be negative which proves the first statement .
 
CASE 2 :
If b < 0 , then a , c must be positive and greater than 0 to give positive value of t where either  a and c can be greater which proves 2nd and 3rd statments . 
Answered by | 19 May, 2012, 02:07: PM

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