Quadratics which arise from observed measurements and experimental results are more likely to need the use of the quadratic formula for solving. The quadratic formula may also demonstrate when no solution exists (something that is difficult to see with factoring). If the coefficient of #x^2# and the coefficient with no #x# element have relatively few factors, time invested in attempting to factor the quadratic is usually worthwhile.Īlso if you know the source of the quadratic, you can sometimes guess if factoring is likely to be successful (for example if it is a simple mathematical model of a situation or a question developed by a friendly math teacher).Īnd you have to be careful with arithmeticīut it will give results when factoring won't work. Or we could add it to both sides, but then you would have to take into account the factored out a. In elementary algebra, the quadratic formula is a formula that provides the two solutions, or roots, to a quadratic equation.There are other ways of solving a quadratic equation instead of using the quadratic formula, such as completing the square. Quadratics with coefficients that involve roots would be one example of "ugly".Īfter that (if the "ugly" rule doesn't apply):įactoring is usually faster and less prone to arithmetic mistakes (if you are working by hand). Now we complete the square using the term (b/a)/2 or b/ (2a), adding and subtracting it to the one side so we don't change the value. The quadratic function y 1 / 2 x 2 5 / 2 x + 2, with roots x 1 and x 4. If the quadratic looks particularly " ugly " use the quadratic formula. The following is mostly some rules of thumb. This is actually a very good question, but not one with a really definitive answer.
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