Algebra Basics, Equations, and Mathematical Models

Essay by toyaplayUniversity, Master'sA+, June 2005

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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).

It is possible to complete a quadratic with an imaginary number. The kind of problematic solutions that would include the use of a quadratic formula ending with an imaginary number would be not be found in normal math or lower algebra. Often, they would found in engineering problems and physics problems.


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?

If there were no formulas to use in "in the real world", many common practices in our every day life would not be understood.

Without formulas, a carpenter would not be able to build a specified item without knowing area or perimeter. Sometimes the exact number is not known. Mathematicians invented the imaginary number to deal with the square roots of negative numbers. In today's world, these numbers are of great use in solving many practical problems, especially in the field of electricity.