If $a, b$ are real numbers and $\alpha$ is a real root of $x^2+12+3 \sin (a+b x)+6 x=0$ then the value of $\cos (a+b \alpha)$ for the least positive value of $a+b \alpha$ is

• A

  -1
• B

  $\frac{1}{\sqrt{2}}$
• C

  $\frac{1}{2}$
• Correct answer
  D

  0

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