# find the interval in which m lies so that the expression mx2+3x-4/-4x2+3x+m can take all real values ,x belongs to R

Arun Kumar IIT Delhi
$\\\frac{mx^2+3x-4}{-4x^2+3x+m}=y \\denominator shouldn't have any roots \\=>3^2-16m<0 \\=>16m>9 \\=>m>\frac{9}{16}$