Suppose a secret sharing scheme is being set up among 5 people. Then 5 shares are distributed to 5 people such that any k = 3 or more can figure out the secret, but 2 or fewer cannot. Lets say we are...

Suppose a secret sharing scheme is being set up among 5 people. Then 5 shares are distributed to 5 people such that any k = 3 or more can figure out the secret, but 2 or fewer cannot. Lets say we are working over GF(7) and the polynomial of degree k1 = 2 are randomly chosen. The shares handed out are P(1) =2 to the first official, P(2)= 2 to the second, P(3) = 1 to the third, P(4) = 6 to the fourth and P(5) = 3 to the fifth official. If official 3, 4 and 5 get together, what is the polynomial P1(x) and the secret S1 they discover? If official 1, 2 and 5 get together, what is the polynomial P2(x) and the secret S2 they discover? Any comments on P1(x) and P2(x) and the two secrets