Let $P$ be a polynomial whose coefficients are real numbers. Suppose the roots of $P(x)=0$ are real. Then

• Correct answer
  A

  the repeated roots of $P(x)=0$ are also roots of $P(x)+P^{\prime}(x)=0$
• B

  the roots of $P(x)+P^{\prime}(x)=0$ are real and distinct
• Correct answer
  C

  the roots of $P(x)+P^{\prime}(x)=0$ are distinct if the roots of $P(x)=0$ are distinct
• Correct answer
  D

  the roots of $P(x)+P^{\prime}(x)=0$ are real

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