SOME polynomials have real roots
In ALL polynomials, when ,
In SOME polynomials . Lets call this condition positive A
In SOME polynomials . Lets call this condition negative A
Here are some possible categories of polynomials;
• polynomials with real roots that are positive A
• polynomials with NO real roots and are positive A
• polynomials with real roots that are negative A
• polynomials with NO real roots and are negative A
Give an example of a polynomial that fits in each category.
Are there polynomials that fit in NONE of these categories? Example, or why not?
Are there polynomials that fit in MORE THAN ONE category? Example, or why not?
Does every possible polynomial fit into at least one of these categories? Why, or why not?
What questions could / would you put to your students based on this applet?