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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
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