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Solve The equation Statement -1 x^(2)+...

Solve The equation
Statement -1 `x^(2)+(2m+1)x+(2n+1)=0` where m and n are integers, cannot have any rational roots.
Statement - 2 The quantity `(2m+1)^2 −4(2n+1)`, where m,n∈I, can never be a perfect square.

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

Text Solution

Verified by Experts

The correct Answer is:
A
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.
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