Is it possible for a fourthdegree polynomial function to hav

Is it possible for a fourth-degree polynomial function to have no real roots?

Solution

Yes it is possible for a 4^th degree polynomial function to have no real roots

example:

let the roots of 4^th degree polynomial be i , -i , 2i , -2i

==> polynomial is (x - i)(x + i)(x - 2i)(x + 2i)

==> (x² +1)(x² +4)

==> x⁴ + 4x² + x² + 4

==> x⁴ + 5x² + 4

x⁴ + 5x² + 4 is 4^th degree polynomial with no real roots