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Make note that some times the discriminant is less than zero. When this is placed in the quadratic formula to find the roots of the equation, the square root of a negative number occurs which means that the equation has no real roots and does not cross the x- axis. In this case we represent the roots using complex or imaginary numbers. For these types of numbers we represent , where i is considered to be an imaginary number. For example if we have as a solution then we write as a complex number in the form .  (Check the discussion in question 55 of the investigation questions)

As a note, mathematicians first referred to these types of numbers as imaginary numbers because they seemed not to exist. However, imaginary numbers do exist and have many applications in the sciences. Despite their name, they are not really imaginary at all. The name dates back to when they were first introduced, before their existence was really understood. At that time, people were imagining what it would be like to have a number system that contained square roots of negative numbers, hence the name "imaginary".