3. (7 points) The graph of a reduced quadratic trinomial is shown in the figure (the y-axis is erased, the distance between adjacent marked points is 1). What is the discriminant of this trinomial?

![](https://cdn.mathpix.com/cropped/2024_05_06_7217c23a0b23cf0b4657g-1.jpg?height=306&width=576&top_left_y=2331&top_left_x=820)
Solution. Let $x_{1}$ and $x_{2}$ be the roots of the given quadratic ( $x_{1}<x_{2}$ ). From the condition, it follows that $x_{2}-x_{1}=2$. Since $x_{2}=\frac{-b+\sqrt{D}}{2}, x_{1}=\frac{-b-\sqrt{D}}{2}$, we get that $x_{2}-x_{1}=\sqrt{D}$, hence $D=4$.

## Answer. 4.