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Eleventh grade Lesson Introduction to Polynomial Equations
A radical equation is an equation in which a variable is under a radical. To solve a radical equation:. Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them. If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation. By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.
In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols;  it is a unifying thread of almost all of mathematics. The more basic parts of algebra are called elementary algebra ; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.
Before proceeding into differential equations we will need one more formula. We will need to know how to take the Laplace transform of a derivative. We now have the following fact. Since we are going to be dealing with second order differential equations it will be convenient to have the Laplace transform of the first two derivatives. The first step in using Laplace transforms to solve an IVP is to take the transform of every term in the differential equation.