The lower quartile of $$f\left(x\right) = \frac{1}{12}\left(5-2x\right); -1 \leq x \leq 2$$ is one root of the quadratic equation:

A

$$Q^{2}_{1} - 3Q_{1} - 5 = 0$$

B

$$Q^{2}_{1} - 5Q_{1} - 3 = 0$$

C

$$Q^{2}_{1} + 5Q_{1} + 3 = 0$$

D

$$Q^{2}_{1} + 3Q_{1} + 5 = 0$$