State whether the following quadratic equations have two distinct real roots. Justify your answer.

${(x-\sqrt{2})}^2-\sqrt{2}(x+1)=0$

State whether the following quadratic equations have two distinct real roots. Justify your answer.

$\sqrt{2}{x}^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$.

State whether the following quadratic equations have two distinct real roots. Justify your answer.

$x(1-x)-2=0$

State whether the following quadratic equations have two distinct real roots. Justify your answer.

$(x-1)(x+2)+2=0$

State whether the following quadratic equations have two distinct real roots. Justify your answer.

$(x+1)(x-2)+x=0$

Every quadratic equation has exactly one root.

Every quadratic equation has atleast one real root.

Every quadratic equation has at least two roots.

Every quadratic equation has utmost two roots.