383(c) α>1/4
Let a,b,c be three distinct real numbers such that the expression ax2+bx+c,
bx2+cx+a, and
cx2+ ax+b
is positive for each x belongs to R
and let α =(bc+ca+ab)/(a2+b2+c2)
Then
(a) α<4
(b) α<1
(c) α>1/4
(d) α>1
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3 Answers
383for (i) eq. b2-4ac>0
for (ii) eq. c2-4ac>0
for (iii) eq. a2-4bc>0
now combine all..........
- Karan Bhuwalka If the expression is positive, how can you say that discriminant is positiveUpvote·0· Reply ·Feb 11 '13 at 19:08
Akash Anand I guess there should be a correction in the equations. All the equations should be less than zero not greater than zero- Soumyabrata Mondal srry ya it suld be '<' instead of ">"
1357Answer is C
Applying AM GM on a, b, c
i.e. a2+b22≥ab
b2+c22≥bc
c2+a22≥ca
adding the three
a2+b2+c2≥ab+bc+ca
- Soumyabrata Mondal den it can be a,b & c
