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In an AP,l th ,m th ,n th terms are 2,4,6 respectively.The equation lx 2 -2mx+n=0 has a.one positive and one negative root b.both roots negative c.imaginary roots d.both roots positive

In an AP,lth,mth,nth terms are 2,4,6 respectively.The equation lx2-2mx+n=0 has


a.one positive and one negative root


b.both roots negative


c.imaginary roots


d.both roots positive

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Menka,

As 2,4,6 are the lth,mth, and nth term. We can write

2 = a+(l-1)d

4 = a+(m-1)d

6 = a+(n-1)d

 

So 4-2 = (m-l)d, 6-4 = (n-m)d

or m-l = n-m, or 2m=l+n.

 

Now discriminant of the QE, D = 4m^2 - 4ln = (l+n)^2 - 4ln = (l-n)^2, which is always positive, and hence roots are real.

 

Now roots = [2m ± (l-n)]/(2l) = [l+n ±(l-n)]/2l = 1, n/l

As l,m,n are positive (as they refer the term number of an AP)

So roots are always positive.

 

Option (D).

 

Hope this helps.

 

Best Regards,

Ashwin (IIT Madras).

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