If the quadratic equation formed by eliminating x from x^2+ x+ =0 and x y+l(x+y)+m=0 has the same roots as that of the given quadratic equation, then the set of values of is

Step-by-step solution

The new quadratic equation formed by after elimination of ' x ' is, aligned & ( l y+m y+l )^2- ( l y+m y+l )+ =0 & (l^2 y^2+m^2+2 l m y )- (l y+m)(y+l) & + (y+l)^2=0 & (l^2- l+ ) y^2+ (2 l m- l^2- m+2 l ) & y+ (m^2- m l+ l^2 )=0 aligned Eq. (i) and x^2+ x+ =0 has same roots, so aligned l^2- l+ 1 & = 2 l m- l^2- m+2 l & = m^2- m l+ l^2 aligned So, l^2- l+ ^2=m^2- m l+ l^2 array rrrl & ^2- (l )-m(m- l) & =0 & ^2- m+ (m- l)-m(m- l) & =0 & ( -m)+(m- l)( -m) & =0 & & =m, l-m array