Quad..

Let a,b,c be natural numbers and the quadratic equation ax²-bx+c=0 have two distinct roots lying in the interval (0,1)...

Now..

a) the least value of a
b) the least value of b
c) the least value of c

[7]

4 Answers

also, b²>4ac because of distinct roots
also, f(0) is +ve so c>0
also f(1) is +ve so a+c>b
f'(0).f'(1)<0
(2a.0-b)(2a1-b)<0
so b(2a-b)>0. b>0 so 2a>b

so in all we have

a+c>b

2a>b

b²>4ac

also nishant bhaiya c>0 so can we take c=1

ye sab to maine bhi laya... par what are there min values... [12]

341

Hari Shankar ·2009-02-13 00:52:58

I have done this earlier in goiit. So i'll just post the link.

See the last post in the thread as the first post does not have a rigorous solution.

http://www.goiit.com/posts/list/algebra-problem-no-3-67916.htm#447898

So a=b=5 and c=1 are the respective minima

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