Number of roots of special polynomials in interval $(0,1)$ I proved that some special class of polynomials has only one root in interval (0,1) 

For example:
$x^{20}+x^{10}+3x^5-30x^{4}+2x+3=0$

Or

$2x^7-10x^5+2x^3+3x+2=0$

Or

$8x^6-2x^5-2x^4-2x^2-1=0$

My question: Is this an interesting result? How can I check for which class of polynomials we know such property?
Note that any polynomial (with real coefficients) which has a (real) root can be scaled and translated so that it has just one root in any given interval [may be a multiple root if the only roots of the original polynomial are multiple roots]. So there has to be some additional feature to make the observation interesting mathematically.

It would be interesting to know what is special about the class you have identified. [It won't form a linear space - the sum of two such polynomials need not have the same property]
Maybe if you say what special kind of polynomials could be an interesting topic ... but my first impression is that the topic looks promising