3. The equation $a x^{2}-b x+c=0$ has two distinct roots $x_{1}, x_{2}$. What is the maximum number of numbers in the set $\left\{a, b, c, x_{1}, x_{2}\right\}$ that can be prime (and, accordingly, natural) numbers? If a prime number appears in the set twice, it should be counted twice. The number 1 is not considered a prime number.
3. Answer: four. Solution. The quadratic trinomial $3 x^{2}-7 x+2$ has roots 2 and $1 / 3$. Therefore, in the set, prime numbers appear four times: 3, 7, 2, 2. All five numbers in the set cannot be prime, since by Vieta's theorem $a x_{1} x_{2}=c$, and a prime number cannot be the product of three primes.

Grading criteria. Correct solution - 7 points. Example without evaluation with accurate identification of prime numbers - 3 points. Evaluation without example - 2 points. In all other cases - 0 points.