[tex]\it Fie\ x_1,\ x_2\in\mathbb{R},\ zerourile\ func\c{\it t}iei \Rightarrow \Delta>0\ \ \ \ \ (1)[/tex]
Distanța dintre rădăcini este:
[tex]\it |x_2-x_1| =\Big|\dfrac{-b+\sqrt{\Delta}-(-b-\sqrt{\Delta})}{2a}\Big| = \Big|\dfrac{2\sqrt{\Delta}}{2a}\Big|\stackrel{(1)}{=}\ \dfrac{\sqrt{\Delta}}{a} =\sqrt{\Delta}\ \ \ \ \ (2)\\ \\ \\ Dar,\ |x_2-x_1|=1\ \ \ \ \ (3)[/tex]
[tex]\it (2),\ (3) \Rightarrow \sqrt{\Delta} =1 \Rightarrow \Delta =1 \Rightarrow m^2-4m=1\Rightarrow m_{1,2}=2\pm\sqrt5[/tex]
