Random copolymers from itaconic acid and/or isomers and sodium alkenyl sulfonates are obtained by polymerization in an aqueous solution via free radicals at an acidic pH in the range from 1.0 to 3.5 and with a redox system as initiator were described. The copolymers can be used as calcium carbonate and calcium, strontium and barium sulfates mineral scale inhibitors and as dispersants of clays, iron oxides, calcium carbonate and strontium, barium and calcium sulfates. Random copolymers prevent and control damage in an oil reservoir, obstruction of water injection and crude oil production pipelines, and in production rigs due to mineral scale precipitation caused by high levels of salinity of the injection water and formation water. Random copolymers are tolerant to high concentrations of divalent ions, such as calcium, magnesium, strontium and barium, and can be added to the reservoir and to injection or production pipelines, treated water, sea water and water that is used as means of transportation. The copolymers can also be used to inhibit and disperse mineral scale occurring in cooling systems and boilers used in the oil and chemistry industry.