n Learning and Teaching Mathematics - Solving cubic equations numerically

Volume 2014, Issue 16
  • ISSN : 1990-6811


For learners who are familiar with the formula for solving quadratic equations, it is greatly disappointing that there isn't a similar method for solving cubic equations. There are of course standard techniques, but these are rather complex and generally not accessible at school level. The types of cubic equations we solve at school typically have at least one integer solution, and this solution (often found by setting up a table of values or using a "guess and check" approach) is used as the basis to finding the other two solutions. This presents the somewhat paradoxical situation that in order to solve a cubic equation you have to know one of the solutions already. But what if the cubic equation doesn't have an integer, or even rational, solution? How would one go about solving such an equation? One would hope that this is exactly the sort of question an engaged student would ask!

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