Hello, I need a polynomial function that is 4th degree with no real roots,
how do I get that?
ty
Basically you want a quadratic that has no real roots. My personal favorite is $\displaystyle x^2+1$
No matter what x you choose it will never equal zero.
Any quadratic of the form $\displaystyle ax^2+bx+c$ 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 $\displaystyle b^2-4ac$
if we check my favorite above its discriminate is
$\displaystyle 0^2-4(1)(1)=-4< 0$ 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
$\displaystyle (x^2+1)^2=x^4+2x^2+1$
I hope this helps you understand a bit better