\(QGT\) is a right triangle where \(m\angle G=90^\circ\). Let the side lengths \(q\), \(g\) and \(t\) of the triangle correspond to the quadratic equation

\[{ qx }^{ 2 }+gx+t=0.\]

Given that the two roots of this equation sum to \(-1.25\) and \(m\angle T=x^\circ\), find the digit product of \(\left\lfloor x \right\rfloor \).

**Details and Assumptions**:

Side \(q\) is opposite to \(m\angle Q\) and so forth

As an explicit example, the digit product of \(25\) is \(2\times 5= 10 \)

\(\left\lfloor x \right\rfloor \) denotes the greatest integer that is less than or equal to \(x\)

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