Which of the following equations has no real roots?

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

$x^2-3x+4=0$

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

$2x^2+x-1=0$

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

$2x^2-6x+\frac{9}{2}=0$

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

$3x^2-4x+1=0$

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

${(x+4)}^2-8x=0$

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.

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