# zeros of polynomials

• Mar 24th 2010, 05:13 PM
bigmac61293
zeros of polynomials
I have a question about the zeros (roots) of polynomials. I have been sick the past couple of days and have a math test tomorrow, so asking my teacher may not be an option tomorrow.

The question(s) is, Is there a possibility that a polynomial function may not have any real solutions or real roots? If so, is there a way of finding the complex roots without a real root to begin with?

• Mar 24th 2010, 07:22 PM
tonio
Quote:

Originally Posted by bigmac61293
I have a question about the zeros (roots) of polynomials. I have been sick the past couple of days and have a math test tomorrow, so asking my teacher may not be an option tomorrow.

The question(s) is, Is there a possibility that a polynomial function may not have any real solutions or real roots?

I assume you mean "real polynomial" , and the answer is yes: $x^2+1\,,\,\,x^4+25, x^2+2x+2$ are just a few examples of an infinity of real polynomial functions without any real root .

If so, is there a way of finding the complex roots without a real root to begin with?

Sometimes there is (the root formula for quadratics, for example), sometimes there isn't a direct one. It all depends on the particular polynomial we're dealing with.

Tonio

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• Mar 24th 2010, 07:34 PM
integral
I also have a great deal of curiosity on this.

If a polynomial has a degree higher than 2, is even, and has more than 2 term... can it be solved? Assuming that it has no real roots.

(Bow)
• Mar 24th 2010, 07:51 PM
tonio
Quote:

Originally Posted by integral
I also have a great deal of curiosity on this.

If a polynomial has a degree higher than 2, is even, and has more than 2 term... can it be solved? Assuming that it has no real roots.

(Bow)

If the degree is 4 then not only can it be solved but we can do it by radicals using the formulae (which are extremely nasty) by Tartagglia and Ferrari. For equations of degree greater than 4 it was proved some 200 years ago that there is NO general formula by radicals to solve them.

Tonio