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    Algebra Basics, Equations, and Mathematical Models

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    1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i).

    Question:
    In the real world, where might these so-called imaginary numbers be used?

    2. When using a formula, we often know the value of one variable to a greater degree of accuracy than we know the others. In your opinion, what affect, if any, does it make on our use of a formula if we know the value of one variable to a greater degree of accuracy than another?

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    Solution Preview

    1. Complex numbers are used in studies of physical phenonomena, for example, a differential
    equation, with coefficients like the a, b, and c in the quadratic formula, that models how electrical circuits or forced spring/damper systems behave. The movement of the shock absorber of a car as it goes over a bump is an example. The behavior of the differential equations depends upon whether the roots of a certain quadratic are complex or real. If ...

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