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Solving Incomplete Equations


Solving an equation means determining your truth set. In solving an incomplete equation, we use factorization techniques and two important properties of real numbers:

1st Property:

2nd Property:

Case 1: type equation .

Example:

  • Determine the roots of the equation , being .
    SolutionInitially we put x in evidence:

    For the product to be zero, one of the factors alone must be. Like this:

    In this way we obtain two roots that form the truth set:

    In general, the equation of type have for solutions and .

2nd Case: type equation

Examples:

  • Determine the roots of the equation , being U = GO.
    Solution:

    In general, the equation of type has two real roots if is a positive number and has no real root if be a negative number.

Next: Solve Complete Equations