Let $f: R \rightarrow R$ be the function $f(x)=\left(x-a_{1}\right)\left(x-a_{2}\right)+\left(x-a_{2}\right)\left(x-a_{3}\right)+\left(x-a_{3}\right)\left(x-a_{1}\right)$ with $a_{1}, a_{2}, a_{3} \in R .$ Then $f(x) \geq 0$ if and only if -

• A

  At least two of $a_{i}, a_{7}, a_{7}$ are equal
• Correct answer
  B

  $a_{i}=a_{i}=a_{7}$
• C

  $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}$ are all distinct
• D

  $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}$, are all positive and distinct

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