$a_{1} x^{2}+b_{1} x+c_{1}=0$ এবং $a_{2} x^{2}+b_{2} x+c_{2}=0$ সমীকরণের উভয় মূলই সাধারণ হওয়ার শর্ত-

$a_{1} b_{2}=a_{2} b_{1}$

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

$a_{1}+a_{2}=b_{1}+b_{2}=c_{1}+c_{2}$

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$