RU-SPB 2017 Problem 91

Sasha's computer can do the following two operations: If you load the card with number $a$ , it will return that card back and also prints another card with number $a+1$ , and if you consecutively load the cards with numbers $a$ and $b$ , it will return them back and also prints cards with all the roots of the quadratic trinomial $x^2+ax+b$ (possibly one, two, or none cards.) Initially, Sasha had only one card with number $s$ . Is it true that, for any $s> 0$ , Sasha can get a card with number $\sqrt{s}$ ?