Question

Mrs. Collins is at the table with you and states that the fourth-degree graphs she has seen have four real zeros. She asks you if it is possible to create a fourth-degree polynomial with only two real zeros. Demonstrate how to do this and explain your steps.

Answer 1

This is one possible thing the graph could look like

Answer 2

There would be two real solutions and two complex ones

Answer 3

Is she looking for a method for creating a polynomial, or just a graph of what it would look like?

Answer 4

both @jabberwock

Answer 5

An example of such polynomial would be (1-x)(1+x)(x^2+1)

f(x) = 0 for x = 1 or x = -1

Answer 6

And the graph would look like this

Answer 7

thank you @ocelot40