Consider the equation $x^2+b x+c=0$, where $b, c$ are integers. Suppose it has an integer solution $p$. Then

• Correct answer
  A

  $p$ is odd, if $c$ is odd.
• B

  $c$ is odd, if $p$ is odd.
• Correct answer
  C

  $b+c$ is odd, if $p$ is odd.
• Correct answer
  D

  $b$ is even, if $b+c$ is even.

Hence, the correct answer is options: 'A', 'C', 'D'.