Let x be a root of the above equation Clearly x notequalto 0

Let x be a root of the above equation. Clearly, x notequalto 0 since 0^2 + 2 middot 0 + 4 notequalto 0. This means that 1 we can divide both sides of the equation by x to get x + 2 + 4/x = 0. Hence, x = -4/x - 2. In the original equation we replace the term \'x\' with -4/x - 2. This results in x^2 + 2 middto (-4/x - 2) + 4 = 0 x^2 - 8/x - 4 + 4 = 0 x^3 - 8 = 0 x = 2. Therefore, x = 2 is a root of x^2 + 2x + 4 = 0.

Solution

This proof is not correct because all instances of x is not substituted in the equation. The equation is x² + 2x + 4 = 0 and you are substituting x with -4/x - 2.

On proper substitution of x, you should get the equation as (-4/x - 2)² +2(-4/x - 2) + 4 = 0

which will reduce to x² + 2x + 4 = 0

When you do not substitute all the instances of any variable in the equation, then it becomes incorrect.