Let $p_1\left(x\right)=x^3-2020x^2+b_{1}x+c_1$ and $p_2\left(x\right)=x^3-2021x^2+b_{2}x+c_2$ be polynomials having two common roots $\alpha$ and $\beta$. Suppose there exist polynomials $q_1\left(x\right)$ and $q_2\left(x\right)$ such that $p_1\left(x\right)q_1\left(x\right)+p_2\left(x\right)q_2\left(x\right)=x^2-3x+2$. Then the correct identity is

• Correct answer
  A

  $p_1\left(3\right)+p_2\left(1\right)+4028=0$
• B

  $p_1\left(3\right)+p_2\left(1\right)+4026=0$
• C

  $p_1\left(2\right)+p_2\left(1\right)+4028=0$
• D

  $p_1\left(1\right)+p_2\left(2\right)+4028=0$

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