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

Hi,
Let assume a and b the 2 real zeroes,
(c+id) and (c-id) the 2 complex zeroes.
P(x)=(x-a)(x-b)(x-(c+id))(x-(c-id))=(x-a)(x-b)((x-c)²-d²) is a fourth-degree polynomial.