# zeros of polynomial on short interval and some reasoning.

I read that polynomial of degree n can have up to n zeros and no more. My question is, which seem very obvious that you might bring number of zeros down by choosing smaller interval. For example -2 to 0 instead of -2 to 2.

Is that correct reasoning ?

• Your reasoning is fine : you are just restricting the domain of the polynomial. This also restricts the preimage of every point in the range of the polynomial, not just zero. – астон вілла олоф мэллбэрг Jan 18 '19 at 5:21

Consider the polynomial $$x^2 + 3x + 2$$. The roots of this polynomial are at $$x = -1$$ and $$x = -2$$, so changing the interval from all real numbers to $$(-\infty, -2]$$ will change the amount of roots $$\text{in that interval}$$.
However, for the same polynomial, if the interval is changed from $$(-\infty, \infty)$$ to $$(-10000, 10000)$$, although the interval changes, the amount of roots in that interval doesn't.