SELECT id , coordinate FROM table_name WHERE MBRContains(GeomFromText('Polygon((-126.728566 49.226434, -123.652395 23.586457,-56.679738 23.908252,-53.076223 55.243002, -126.728566 49.226434))'), coordinate)
This should work. The problem is that Polygon coordinates should be in double parenthesis. It has something to do about interior rings (polygons). Plus as David noticed You need to close polygon.
PS: I noticed You use longitude as X and latitude as Y when this should be other way around. X are horizontal and Y vertical.