Very Interesting

JEE Main 2015 Help › Algebra questions › Very Interesting

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 Î± =(bc+ca+ab)/(a²+b²+c²)

Then
(a) Î±<4
(b) Î±<1
(c) Î±>1/4
(d) Î±>1

#Mathematics #Algebra

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3 Answers

383

Soumyabrata Mondal ·2013-02-11 08:44:05

(c) Î±>1/4

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383

Soumyabrata Mondal ·2013-02-11 08:47:08

for (i) eq. b²-4ac>0
for (ii) eq. c²-4ac>0
for (iii) eq. a²-4bc>0

now combine all..........

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Karan Bhuwalka If the expression is positive, how can you say that discriminant is positive
Upvote·0· Reply ·2013-02-11 19:08:38
Akash Anand I guess there should be a correction in the equations. All the equations should be less than zero not greater than zero
Upvote·0· Reply ·2013-02-12 06:16:00
Soumyabrata Mondal srry ya it suld be '<' instead of ">"
Upvote·0· Reply ·2013-02-14 07:31:28
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1357

Manish Shankar ·2013-02-14 05:06:52

Answer is C

Applying AM GM on a, b, c

i.e. a²+b²2â‰¥ab
b²+c²2â‰¥bc
c²+a²2â‰¥ca

adding the three
a²+b²+c²â‰¥ab+bc+ca

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Soumyabrata Mondal den it can be a,b & c
Upvote·0· Reply ·2013-02-14 07:29:12
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