Statement (A): 1 and 2 are the roots of ${\text{x}}^{\text{2}}\text{-3x+2=0}$ 

Statement (B): The quadratic equation whose roots are $\alpha ,\beta$ is $x^2+\left(\alpha +\beta \right)x+\alpha \beta =0$

I)1 and 2 are roots or  ${\text{x}}^{\text{2}}\text{-3x+2=0}$

${\text{x}}^{\text{2}}\text{-3x+2=0}$  

$here$   $\text{a=1,}\text{b= -3,}\text{c=2}$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{3\pm \sqrt{{\left(-3\right)}^2-4\left(1\right)\left(2\right)}}{2\times 1}$

$=\frac{3\pm \sqrt{9-8}}{2}$

$=\frac{3+1}{2}$

$x=\frac{3+1}{2}or\frac{3-1}{2}$

$x=2orx=1$

II) The quadratic equation whose roots are

$\alpha ,\beta$  is  $x^2+\left(\alpha +\beta \right)x+\alpha \beta =0$

False because

Sum of the roots  $=\frac{\mathrm{co}-efficientofx}{co-efficient{x}^2}$

$\left(\alpha +\beta \right)=\frac{-\left(\alpha +\beta \right)}{1}$

$\left(\alpha +\beta \right)=-\left(\alpha +\beta \right)$  which is not possible