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ground zero - the point of detonation (or above or below) of a nuclear weapon. point - the precise location of something; a spatially limited location; she walked to a point where she could survey the whole street.
To find the places where the field is zero, simply add the field from the first charge to that of the second charge and see where they cancel each other out. In any problem like this it's helpful to come up with a rough estimate of where the point, or points, where the field is zero is/are.