If for a non - zero x, 3x2 + 5x + 3 = 0, then the value of x^3 + 1x^3 is?

Answer: Option A

$$\begin{array}{rl}& 3x^2+5x+3=0\\ & 3x^2+3=-5x\\ & \text{Divide by }3x\text{ both sides}\\ & x+\frac{1}{x}=\frac{-5}{3}\\ & \text{Then, }{x}^3+\frac{1}{x^3}\\ & ={\left(\frac{-5}{3}\right)}^3-3\times \left(\frac{-5}{3}\right)\\ & =\frac{-125}{27}+5\\ & =\frac{10}{27}\end{array}$$