যে শর্ত সাপেক্ষে $a_{1} x^{2}+b_{1} x+c_{1}=0$ এবং সমীকরণ $a_{2} x^{2}+b_{2} x+c_{2}=0$ দুটির একটি সাধারণ মূল থাকবে?

$\left(b_{1} c_{2}-b_{2} c_{1}\right)\left(c_{1} a_{2}-c_{2} a_{1}\right)=\left(a_{1} b_{2}-a_{2} b_{1}\right)^{2}$

$\left(b_{1} c_{2}-b_{2} c_{1}\right)\left(c_{1} a_{2}-c_{2} a_{1}\right)=\left(a_{1} b_{2}-a_{2} b_{1}\right)$

$\left(a_{1} b_{2}-a_{2} b_{1}\right)\left(c_{1} a_{2}-c_{2} a_{1}\right)=\left(b_{1} c_{2}-b_{2} c_{1}\right)^{2}$

$\left(b_{1} c_{2}-b_{2} c_{1}\right)\left(a_{1} b_{2}-a_{2} b_{1}\right)=\left(c_{1} a_{2}-c_{2} a_{1}\right)^{2}$