# The Binary Root

Algebra Level 5

$x^2-px+q=0$

is called binary-quadratic if it satisfy the following conditions:

• All digits of the non-negative integers $$p$$ and $$q$$ are either $$0$$ or $$1$$

• All digits of the roots are either $$0$$ or $$1$$

How many binary-quadratic equations are there such that both roots are smaller than $$10^4$$.

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