# polynomial fuction

• May 12th 2009, 08:17 PM
cokeclassic
polynomial fuction
Hello, I need a polynomial function that is 4th degree with no real roots,
how do I get that?
ty
• May 12th 2009, 08:19 PM
TheEmptySet
Quote:

Originally Posted by cokeclassic
Hello, I need a polynomial function that is 4th degree with no real roots,
how do I get that?
ty

Do you know of a polynomial with degree 2 that has no real roots(Wink). If so square it and you are done. if you dont just ask
• May 12th 2009, 08:40 PM
cokeclassic
Um I am not sure what I am even doing so, no I dont
• May 12th 2009, 09:03 PM
TheEmptySet
Quote:

Originally Posted by cokeclassic
Um I am not sure what I am even doing so, no I dont

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