I got this function right here and my teacher wants me to find all real number zeros
$$10x^2+20x+19x+97^1.$$
I looked up this video on how to find it and they were using the $P/Q$ and I found the factors of $97$ and $10$ and them divided them and those were supposed to be the possible zeros, I then did the same thing they did and none of the numbers I got got me zero when I plugged it in, maybe I'm just doing it wrong?
If your polynomial is indeed what you have written, then
$$10x^{2}+39x+97=0$$
Is simply a quadratic polynomial, so we can apply the quadratic formula, that is
$$x=\frac{ -39 \pm\sqrt{(39)^{2}-4(10)(97)}}{20}$$
Which will yield two complex solutions , no real so most likely you wrote this incorrectly