what is the condition of common root and roots of two  quadrataic equations?

Solve : k/(x+k+m) +j/(x+j+m)=1 has equal and of opposite sign,then m=

             1)0      2)1      3)-1       4)2

ans:(1) 

Rewrite the given expn as the normal quadratic form and apply the condition that

thus u will get the answer

after solving the it u will get a quadratic  equation i.e.

x^2+mx+(m^2-jk)=0

 since,the roots are of equal and opposite sign

thier sum will be equal to 0.

i.e -m=0

m=0 ans...