If p and q are roots of the quadratic equation x^2 + mx + m^2 + a = 0, then find the value of p^2 + q^2 + pq.

We have the quadratic equation in x, x^2 + mx + m^2 + a = 0, and its given that it has roots p and q.

So, 
sum of roots = p + q = -m/1 = -m
product of roots = pq = m^2 + a

We have to find the value of p^2 + q^2 + pq

p^2 + q^2 + pq
= (p + q)^2 - pq

Now, we'll use the values of (p + q) and pq we calculated above;

= (-m)^2 - (m^2 + a)
= m^2 - m^2 - a
= -a

Hence, the value of p^2 + q^2 + pq is -a