Question

A polynomial with complex zeros never crosses or touches the x-axis.. Why is this incorrect??

Answer 1

because it may have real zeros as well?

Answer 2

It may have real roots, not only complex. That's not stated in the problem.

Answer 3

For example, x^3 - 5x^2 + x - 5 has two complex roots and one real root.

It can be rewritten as (x-i)(x+i)(x-5).

If you look at the graph, it begins at negative infinity, and as x increases it moves up, but before reaching the x axis it "turns around" and start moving away again. Finally it "turns around" and crosses the x axis at x=5, and then goes on to infinity.

Answer 4

That little "turning around" maneuver it pulled without crossing the x axis, that is what indicates a pair of complex roots.

Answer 5

You can see the picture here
http://www.wolframalpha.com/input/?i=%28x-i%29%28x%2Bi%29%28x-5%29

Answer 6

thank you so much :)

Answer 7

cool :p