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Let S be the sum of all possible determi...

Let S be the sum of all possible determinants of order 2 having 0,1,2 and 3 as their elements,. Find the common root `alpha` of the equations `x^(2)+ax+[m+1]=0,`
`x^(2)+bx+[m+4]=0`
and `x^(2)-cx+[m+15]=0`
such that `alphagtS`wherea+b+c=0 and
`m=lim_(n to 00)(1)/(n)sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2)))`
and [.] denotes the greates integer function.

Text Solution

Verified by Experts

The correct Answer is:
`=sqrt(5)-1`
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