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` where a+b+c=0 and
`m=sum_(n to 00)(1)/(n)sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2)))`
and [.] denotes the greates integer function.

Similar Questions

Explore conceptually related problems

lim_(n rarr oo) sum_(r=0)^(n-1) 1/(sqrt(n^(2)-r^(2))) =

Find the sum of roots of quadratic equations ax^(2) +bx+ c=0

lim_(n rarr oo) sum_(r=1)^(n) r/n^(2) sec^(2) (r^(2)/n^(2)) =

lim_(n rarr oo) n.sum_(r=0)^(n-1) 1/(n^(2)+r^(2)) =

lim_(n to oo) 1/(n^2) sum_(r = 1)^(n) re^(r//n) equals :

lim_(n rarr oo) (1)/(n^(3)) sum_(r = 1)^(n) r^(2) is :

If m and n are the roots of the equations 2x^(2)- 4x + 1=0 Find the value of (m+n) ^(2) +4mn.

lim_(n to oo) sum_(r = 1)^(n) 1/n sin(r pi)/(2pi) is :

If m and n are roots of equations 2x^(2) - 6x +1=0 , then the value of m^(2) n+ mn ^(2) is: