Basically you want a quadratic that has no real roots. My personal favorite is
No matter what x you choose it will never equal zero.
Any quadratic of the form will have no real roots if the discriminate is negative.
The discriminate is the part of the quadratic formula under the square root. eg this part
if we check my favorite above its discriminate is
so it have no real roots.
If you square a polynomial you don't change its roots just how many times they are repeated so to get a fourth degree just square my favorite above
I hope this helps you understand a bit better