If \( \frac{2}{L}, \frac{2}{m} \) are the two roots of the equation \( 4 x^{2}+3 x-2=0 \) find the quadratic equation of roots \( L, m \).

a) \( \left(3^{6}\right)^{7} \cdot 3^{2}: 3^{41}-5^{2}= \) c) \( \left[\left(2^{2}\right)^{3}\right]^{3}:\left(2^{3}\right)^{5}= \) e) \( 4^{3} \cdot\left(4^{5}\right)^{4}:\left(4^{3}\right)^{7}-2^{4}= \) g) \( \left[\left(5^{3}\right)^{12}:\left(5^{2}\right)^{17}-25\right]: 5= \) i) \( \left.2^{6}+10 \cdot\left[3 \cdot 3^{3}-\left(3^{4}\right)^{3}: 3^{11}\right)\right]= \)

d) \( \frac{3^{4}: 3}{3^{2}}= \)

Aplica el método de fracciones parciales a la función: \( \frac{x^2 + 2}{(x-1)(x+3)} \)

Analizar y graficar 3) \( y=2 x^{2}-4 x+5 \)

e) \( \sqrt[2]{2} \cdot \sqrt[2]{18}= \)