What are the zeros if f of x equals x root 2 plus 4x plus 8?

To find the zeros of the function ( f(x) = x\sqrt{2} + 4x + 8 ), we set the equation equal to zero: ( x\sqrt{2} + 4x + 8 = 0 ). This can be rewritten as ( x(\sqrt{2} + 4) + 8 = 0 ). Solving for ( x ), we get ( x(\sqrt{2} + 4) = -8 ), leading to ( x = \frac{-8}{\sqrt{2} + 4} ). Thus, the zeros of the function are ( x = \frac{-8}{\sqrt{2} + 4} ).