If the roots of the equation  m + (2m-1)x + m - 2 = 0   are rational, then if m I  it will be:

1. odd integer


2. even integer


3. onle zero


4. none of these

Plz explain also.

THanks

for the roots to b rational D shud b a perfect square 

First see http://www.goiit.com/posts/list/algebra-if-a-b-and-c-are-odd-integers-prove-that-the-quadratic-39033.htm

From this you can see that the quadratic   cannot have rational roots if all of a,b and c are odd.

here b = 2m-1 is odd and with a= m and c = m-2, if m is odd both a and c become odd.

Hence, we must have m even.

This question that if  has rational roots then a,b and c cannot all be odd has a simpler explanation than the one given in the link above

Suppose a,b and c are all odd.

Then from rational roots theorem (see wikipedia for this very instructive theorem), if the root is of the form p/q, then p divides c and q divides a.

This of course means that p and q are both odd. Now, if you substitute x = p/q and multiply by , then you get

  i.e. the sum of 3 odd integers = 0 which is a contradiction.

@utsav,for the roots to be real.D must be a perfect square bcoz,

The roots of the quadratic ax²+bx+c=0 are -b/2a/2a.So,for the roots to be rational,D must be a perfect square.