Question

is it 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 possible, if two zeros are real numbers and the other two zeros are complex numbers.

Example: (x-1)(x+1)(x^2 + 1) = 0

or (x^2-1)(x^2+1) = 0

The real zeros are 1 and -1; the complex zeros are i and - 1.

Because when you set x^2 + 1 = 0, you get x^2 = -1, and only i and -i are solutions.

x^2 - 1 = 0 has two real zeros, x = 1 and -1.

Answer 2

thank you