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

For the presented problem, let’s say for the example (x^2-a^2)^2, the roots are only a and -a, but it may be possible that they’d count each root twice but can be prevented if they’re looking at the graph. You can actually make out two real zeroes and two imaginary ones from the example. (x+1)(x-1)(x+i)(x-i) is (x^2-1)(x^2+1)= x^4-1. I am hoping that this answer has satisfied your query about this specific question.