If $\alpha, \beta$ are the roots of the equation $x^2+3 x+\mathrm{k}=0$ and $\alpha+\frac{1}{\alpha}, \beta+\frac{1}{\beta}$ are the roots of the equation $4 x^2+p x+18=0$ then k satisfies the equation

• Correct answer
  A

  $2 x^2-13 x+20=0$
• B

  $x^2-5 x+6=0$
• C

  $2 x^2-7 x+3=0$
• D

  $x^2-8 x+15=0$

Hence, the correct answer is option: 'A'.