# Solutions or Roots of Quadratic Equations  A real number x will be called a solution or a root if it satisfies the equation, meaning . It is easy to see that the roots are exactly the x-intercepts of the quadratic function , that is the intersection between the graph of the quadratic function with the x-axis.

 a<0 a>0  Example 1: Find the roots of the equation Solution. This equation is equivalent to Since 1 has two square-roots , the solutions for this equation are Example 2: Find the roots of the equation Solution. This example is somehow trickier than the previous one but we will see how to work it out in the general case. First note that we have Therefore the equation is equivalent to which is the same as Since 3 has two square-roots , we get which give the solutions to the equation We may then wonder whether any quadratic equation may be reduced to the simplest ones described in the previous examples. The answer is somehow more complicated but it was known for a very longtime (to the Babylonians about 2000 B.C. ). Their idea was based mainly on completing the square which we did in solving the second example. [Algebra] [Complex Variables]
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Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard. Author: Mohamed Amine Khamsi