Sketch a graph, y = f(x), that has the number and types of roots described for each situation below. Homework Help ✎
Five real roots
Three real and two complex roots
Four complex roots
Four complex and two real roots
Since the degree is an odd number, it will start and end in different directions.
A real root occurs when the polynomial intersects the x-axis, so this graph should intersect the x-axis 5 times.
This polynomial has 5 roots, but only 3 x-intercepts.
A possible graph would be a polynomial with 3 x-intercepts plus another bend.
The degree of this polynomial is even, so it starts and ends in the same direction.
See part (a), (b), and (c).