# Quadratic Formula Research Paper

A quadratic equation is a second order, univariate polynomial with constant coefficients and can usually be written in the form: *ax*^{2} + *bx* + *c* = 0, where *a* 0. In about 400 B.C. the Babylonians developed an algorithmic approach to solving problems that give rise to a quadratic equation. This method is based on the method of **completing the square**. Quadratic **equations**, or **polynomials** of second-degree, have two **roots** that are given by the quadratic formula: *x* = (-*b* +/- (*b*^{2} - 4*ac*))/2*a*. There is another form of this equation yielding the roots for a quadratic equation that is obtained by first dividing the original quadratic equation through by *x*: *x* = (2*c*)/(-*b* +/- (*b*^{2} - 4*ac*)). This equation, which provides the roots to the quadratic equation, is often useful when *b*^{2} > 4*ac*. In these cases the usual form providing roots to the quadratic equation can yield erroneous...

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This is a case study investigating ten Year 11 repeating students’ strategies in solving three selected sub-topics in algebra; changing the subject of a given formula, factorising quadratic expressions and solving quadratic equations using quadratic formula. Specifically, students’ error patterns in solving these topics were identified through qualitative analysis of students’ written answers to a given test and through interviews which revealed students’ thinking and strategies used in solving the given algebraic problems. Errors made by the students were analysed for patterns and their causes. Some of the origins of errors include the failure to manipulate operations correctly in changing the subject of a given formula, the incorrect selection of multiplication factors in the factorisation of quadratic expressions, and the inability to recall correct quadratic formula in solving quadratic equations. There were other psychological factors noted as well such as carelessness and participants’ lack of confidence in answering the questions.

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