Question

Determine whether the given values are the solutions of the given equation or not. $x^2-\sqrt{2}x-4=0;x=-\sqrt{2},x=-2\sqrt{2}$

• A. Only $x=-\sqrt{2}$ is the solution of the equation
• B. Only $x=-2\sqrt{2}$ is the solution of the equation
• C. Both $x=-\sqrt{2},-2\sqrt{2}$ are the solutions of the equation
• D. None of these

Answer 1

The correct option is A Only $x=-\sqrt{2}$ is the solution of the equation

$x^2-\sqrt{2}x-4=0$
$x^2-2\sqrt{2}x+\sqrt{2}x-4=0$
$x(x-2\sqrt{2})+\sqrt{2}(x-2\sqrt{2})=0$
$(x+\sqrt{2})(x-2\sqrt{2})=0$
$x=-\sqrt{2}$ and $x=2\sqrt{2}$
Hence out of the two $x=-2\sqrt{2}$ is not a solution.