Explanation:

To solve this, we need to analyze the conditions given:

 C is a single-digit prime greater than 2. Possible values: 3, 5, or 7.

- P is a two-digit prime number less than 20 and greater than 11. The only possibility is 13,17

-B is a two-digit prime number less than 20 and greater than 13. The only possibility is 17,19

- Since the smallest roots of both equations are the same and none of the roots are irrational:

- This suggests the discriminants of both equations should be perfect squares.

- 3c > b so the possible is only c = 7 , p=17,B=19

-  q = b + 1

q = 19+ 1 = 20

so p × q=17*20=340