Hello, I need a polynomial function that is 4th degree with no real roots,

how do I get that?

ty

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- May 12th 2009, 08:17 PMcokeclassicpolynomial 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 PMTheEmptySet
- May 12th 2009, 08:40 PMcokeclassic
Um I am not sure what I am even doing so, no I dont

- May 12th 2009, 09:03 PMTheEmptySet
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