What is a quartic polynomial function with rational coefficients and roots of ±2 and 5i ?

Answer 1

A quartic polynomial contains a variable with the highest degree of 4.

If ± 2 are roots then:

(x ± 2) are factors

Multiplied together they become:

(x + 2)(x – 2) = x2 - 4

If 5i is a root, then -5i must also be a root. So similarly:

x ± 5i are factors

Multiplied together they become:

(x + 5i)(x – 5i) = x² + 25

Combined the polynomial becomes:

(x² – 4)( x² + 25) =

x⁴ + 21x² - 100