If the equations $x^2-p x+q=0$ and $x^2-a x+b=0$ have a common root and the roots of the second equation are equal, then which one of the following is correct?

• A

  $a q=2(b+p)$
• B

  $a q=b+p$
• Correct answer
  C

  $a p=2(b+q)$
• D

  $a p=b+q$

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