Home
Class 12
MATHS
The equation satement 1:x^(2)+(2m+1)x+...

The equation
satement 1:`x^(2)+(2m+1)x+(2n+1)=0`where m and n are integers, cannot have any rational roots.
Statement2: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.
Promotional Banner

Similar Questions

Explore conceptually related problems

If the equation (1+m)x^(2)-2(1+3m)x+(1-8m)=0 where m epsilonR~{-1} , has atleast one root is negative, then

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

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

The coefficients of x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

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

If m and n are the roots of the equations x^(2) -3x +4 =0 then find the value of m^(2)n+mn^(2)

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

If m and n are the roots of the quadratic equations x^(2) - 3x+1 =0 , then find the value of (m)/( n) + ( n)/(m)