If 2x2 + 5x + 1 = 0, then one of the value of x - 12x is:

Answer: Option A

$$\begin{array}{rl}& 2x^2+5x+1=0\\ & 2x^2+1=-5x\\ & 2x+\frac{1}{x}=-5\\ & \text{divide ’2’ both sides}\\ & x+\frac{1}{2x}=-\frac{5}{2}\\ & a-b=\sqrt{{\left(a+b\right)}^2-4ab}\\ & x-\frac{1}{2x}=\sqrt{{\left(-\frac{5}{2}\right)}^2-4\times x\times \frac{1}{2x}}\\ & =\sqrt{\frac{25}{2}-2}\\ & =\frac{\sqrt{17}}{2}\end{array}$$