Aus Online Mathematik Brückenkurs 1

The equation \displaystyle \left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=0 is a second-degree equation which has \displaystyle x=\text{3 } and \displaystyle x=\sqrt{\text{3}} as roots; when \displaystyle x=\text{3 }, the first factor is zero and when \displaystyle x=\sqrt{\text{3}} the second factor is zero.

If we expand the equations left-hand side, we get the equation in standard form,

\displaystyle \begin{align} & \left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=x^{2}-\sqrt{\text{3}}x-3x+3\sqrt{\text{3}} \\ & =x^{2}-\left( 3+\sqrt{\text{3}} \right)x+3\sqrt{\text{3}}=0 \\ \end{align}

NOTE: the general answer is,

\displaystyle ax^{2}-\left( 3+\sqrt{\text{3}} \right)ax+3\sqrt{\text{3}}a=0

where \displaystyle a\ne 0 is a constant.