The Binary Root

Algebra Level 5

A quadratic equation

\[x^2-px+q=0\]

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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