• RandomRationalQuadraticFactoring.xls: Quadratic equations with rational roots

• RandomIntegerQuadraticFactoring.xls: Quadratic equations with integer roots

Random Worksheets: Factoring Quadratic Equations

So after creating worksheets to generate random multiplication problems (RandomMultiplicationWorksheets), I decided to try a harder problem: random quadratic equation factoring problems. This was trickier, because you can't give the terms random coefficients and expect the resulting equation to be solvable with real numbers.

Example worksheet

Example answer sheet

Notes

• The sample pages have problems with integer roots, and were generated by RandomIntegerQuadraticFactoring^?.xls, attached at the bottom of the page.

• The second attached spreadsheet generates problems with rational roots, though be aware that I've made no attempt to reduce the fractional answers to their simplest form. This is RandomRationalQuadraticFactoring^?.xls, also attached at the bottom of the page.

• To create a new worksheet, recalculate the spreadsheet and print. To recalculate a spreadsheet in Excel, press F9.

• Don't try to do problems on the computer version of the worksheet. Every time you change a cell, the spreadsheet will recalculate and change all the problems (unless you have automatic recalculation turned off.) This is intended to create pencil and paper worksheets.

• One of the problems with random worksheets is associating the worksheet with its corresponding answer sheet. To do that, I've included both a title and a random serial number. In theory, it is possible that you will get two different worksheets with the same serial number and title, but the probability seems adequately low to me.

• Calculation is done on the problem sheet in this spreadsheet.

The Details

I won't go into quite the detail I went into on the RandomMultiplicationWorksheets, but I'll mention a few things, in case someone wants to play around.

Since the constraints were on the answers rather than the question, I decided to randomize the answers and generate the questions from the random answers. While this was far easier than the reverse, there were still a couple of significant constraints:

• I couldn't have a coefficient of "0" for either "x", because the result would be undefined.

• I wanted both negative and positive coefficients.

I also wanted to present both the problems and answers in a form that would be fairly easy to understand. Specifically, I wanted to not see, "x + (-7) = 0".

The result is a bit of a kludge:

• I showed most numbers as their absolute values and printed the appropriate sign (- or +) using an IF statement.

• I generated the signs and the absolute values of the x coefficients with separate randomizers.

• I used values in hidden cells that are referenced elsewhere.

As you might expect, the spreadsheets were difficult to debug, so if you notice any problems, let me know so I can fix them.

-- DougSundseth - 28 Oct 2005

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