Approximate Roots

Equation

Degree

Sketch

Approximate roots

5*+4-0

In Exercise 1, how many real roots did you find for polynomial equations of degree 2? of degree 3? of degree 4? ' Make a conjecture relating the number of real roots and the degree of a polynomial equation. ; Use the results of Exercise 1 and try additional equations as needed to answer the following questions. a. "Does the graph of a second-degree polynomial equation always intersect Hie jtf-axis in two places? b. Does the graph of a second-degree polynomial equation always intersect the jo-axis at least once?_; c. If a second-degree polynomial equation does not intersect the x-axls, what is true about the roots of that equation? d. Does a third-degree polynomial equation always intersect the jo-axis in three places? : r. . . e. Does a third-degree polynomial equation always have three real roots?. 3. Experiment with the graphs of polynomial equations of degree greater than four. Make a conjecture about the maximum number of real roots and the degree of a polynomial equation, ,_,.,-

ACTIVITY 21-