Probability of Root Placement

Algebra Level 4

$$k$$ is uniformly chosen from the interval $$[ -5, 5]$$. Let $$p$$ be the probability that the quadratic $$f(x) = x^2 + kx + 1$$ has both roots between -2 and 4. What is the value of $$\lfloor 1000 p \rfloor$$?

Details and assumptions

Greatest Integer Function: $$\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$$ refers to the greatest integer less than or equal to $$x$$. For example $$\lfloor 2.3 \rfloor = 2$$ and $$\lfloor -3.4 \rfloor = -4$$.

×