B1. Solve the inequality $-\frac{1}{2} x^{2}+x+\frac{15}{2} \leq 0$.
B1. Solve the quadratic inequality graphically. Find the roots $x_{1}=5, x_{2}=-3$, and represent the solution graphically. Read off the appropriate intervals and write $(-\infty,-3] \bigcup[5, \infty)$.

Write the equation $-\frac{1}{2} x^{2}+x+\frac{15}{2}=0$ 1 point

Rearrange the equation $x^{2}-2 x-15=0$... 1 point

Factorization $(x-5)(x+3)=0$ 1 point

Roots $x_{1}=5, x_{2}=-3$ .1 point

![](https://cdn.mathpix.com/cropped/2024_06_07_bce9c6e2a6f4f88bb0deg-14.jpg?height=369&width=379&top_left_y=224&top_left_x=1538)

Graphical representation 1 point

Answer $(-\infty,-3] \bigcup[5, \infty)$