Task 4. (Option 2)

For what values of $a$ does the inequality $x^{2}<4-|x-a|$ have at least one negative solution?
Solution: On the plane $x O a$, plot the set of points whose coordinates satisfy the inequality $x^{2}x^{2}+x-4$; when $x-a<0$, the form is $a<-x^{2}+x+4$. In the shaded area, points with positive abscissas exist when $a \in\left[-\frac{17}{4} ; 4\right)$.

![](https://cdn.mathpix.com/cropped/2024_05_06_96a99fe03936e779e014g-05.jpg?height=677&width=740&top_left_y=1712&top_left_x=1206)

Answer: $a \in\left[-\frac{17}{4} ; 4\right)$