# 50 Follower Special

Geometry Level 4

$$QGT$$ 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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