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businesses would use them to predict trends in data and statisticians would use them to extrapolate the results of a sample group of a study or survey.
Very much so. The result is gratifying in its obvious reflection of the real world situation embodied in the problem.
you can have either one or three x-intercepts, but now 2. because two real roots means 1 imaginary root which is not possible since imaginary roots come in pairs (2,4,6,8...)
The negative solutions are often discard because they have no real meaning in the real world, for example, you can not have -6 apples, it just doesn't make sense.
A fjord is a real world example of a fjord! They exist in the real world.