Statement -1 The equation
`x^(2)+(2m+1)x+(2n+1)=0` where `m,n epsilonI` canot have any rational roots.
Statement -2 The quantity `(2m+1)^(2)-4(2n+1)`, where `m, n epsilonI` can never be perfect square.

Options

A. Statement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement-1
B. Statement -1 is true, Statement -2 is true, Statement -2 is not a correct explanation for Statement -1
C. Statement -1 is true, Statement -2 is false
D. Statement -1 is false, Statement -2 is true

Answer

A

Explanation

We have `x^(2)+(2m+1)x+(2n+1)=0`…….i
`m,n epsilon I`
`:.D=b^(2)-4ac`
`=(2m+1)^(2)-4(2n+1)`
is never be a perfect square.
Therefore, the roots of Eq. (i) can never be integers. Hence the roots of Eq. (i) cannot have any rational as `a=1,b, c epsilon I`. Hence both statement are true and statements-2 is a correct explanatioin of Statement -1.