14. The two roots of the quadratic equation
$$
x^{2}-85 x+c=0
$$
are both prime numbers. What is the sum of the digits of $c$ ?
A 12
B 13
C 14
D 15
E 21
14. B Suppose the quadratic has roots $p$ and $q$. So it factorises as $(x-p)(x-q)$. This expands to give $x^{2}-(p+q) x+p q$. Comparing this with $x^{2}-85 x+c$ shows that $p+q=85$ and $p q=c$. It follows that one of $p, q$ is even and one is odd. The only even prime is 2 so the primes $p, q$ are 2 and 83 . Therefore $c=2 \times 83=166$, and therefore has digit sum 13 .