# Two positive real roots

Algebra Level 4

A quadratic equation $$x^{2} -10x -5 = ax + b$$ has two positive real roots $$\alpha$$ and $$\beta.$$ Define $$p$$ as the minimum possible integer value of $$a ,$$ and define $$q$$ as the minimum value of $$\alpha ^{2} + \beta ^{2}.$$ What is $$pq?$$

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