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

It is. The simplest example of it would be by "creating" it by multiplying two terms in the form of (x-p)(x-q) and one wich is grade two and has no real zeroes (easiest option would be x^2+k^2, but anything in the form ax^2 +bx +c *if and only if* b^2-4ac <0 goes well)

Answer 2

Thank you