[i][b]SOME[/b][/i] polynomials have real roots[br][br]In [i][b]ALL[/b][/i] polynomials, when [math]\left|x\right|\longrightarrow\infty[/math],[math]\left|f\left(x\right)\right|\longrightarrow\infty[/math][br][br]In [i][b]SOME[/b][/i] polynomials [math]f\left(x\longrightarrow\infty\right)\cdot f\left(x\longrightarrow-\infty\right)>0[/math]. Lets call this condition [i][b]positive A[/b][/i][br][br]In [i][b]SOME[/b][/i] polynomials [math]f\left(x\longrightarrow\infty\right)\cdot f\left(x\longrightarrow-\infty\right)<0[/math]. Lets call this condition[i][b] negative A[/b][/i][br][br]Here are some possible categories of polynomials;[br][br] • polynomials with real roots that are [b]positive A[/b][br] • polynomials with [b]NO[/b] real roots and are [b]positive A[/b][br] • polynomials with real roots that are [b]negative A[/b][br] • polynomials with [b]NO[/b] real roots and are [b]negative A[/b][br][br]Give an example of a polynomial that fits in each category.[br][br]Are there polynomials that fit in [b]NONE [/b]of these categories? Example, or why not?[br][br]Are there polynomials that fit in [b]MORE THAN ONE[/b] category? Example, or why not?[br][br]Does every possible polynomial fit into at least one of these categories? Why, or why not?[br][br][color=#ff0000][i][b]What questions could / would you put to your students based on this applet? [/b][/i][/color][br]

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