The product of the roots of the equation x2−4mx+3e2logm−4=0  is 8, then its roots will be real when m  equals

The given equation is x2−4mx+3e2logm−4=0 Given that, product of the roots =8⇒  3e2logm−4=8⇒  3elogm2=12  ⇒  m2=4⇒  m=±2 ..Now the given equation becomes x2−4mx+3m2−4=0Its roots are real if 16m2−43m2−4≥0    (∵  b2−4ac≥0)If4m2+16≥0 , which is true if m=±2 .Hencem=±2 .