If $x=\sqrt{2}$ is one of the roots of the equation $ax^{2}+\sqrt{2}bx+2c=0$; $a \neq 0$,$a, b, c \in R$,then prove that $a+b+c=0$.

(N/A) Given that $x=\sqrt{2}$ is one of the roots of the quadratic equation $ax^{2}+\sqrt{2}bx+2c=0$.
Since $x=\sqrt{2}$ is a root,it must satisfy the equation.
Substituting $x=\sqrt{2}$ into the equation:
$a(\sqrt{2})^{2} + \sqrt{2}b(\sqrt{2}) + 2c = 0$
Simplifying the terms:
$a(2) + 2b + 2c = 0$
$2a + 2b + 2c = 0$
Dividing the entire equation by $2$:
$a + b + c = 0$
Hence,it is proved that $a+b+c=0$.