8. Find all real solutions. Show work. \[ 0=4 x^{4}-12 x^{2} \]

To solve the equation \( 0 = 4x^4 - 12x^2 \), let's factor it. First, we can factor out common terms: \[ 0 = 4x^2(x^2 - 3) \] Now we have a product of two factors equal to zero. For the product to be zero, at least one of the factors must equal zero. This gives us two equations to solve: 1. \( 4x^2 = 0 \) 2. \( x^2 - 3 = 0 \) For the first equation, \( 4x^2 = 0 \): \[ x^2 = 0 \] \[ x = 0 \] For the second equation, \( x^2 - 3 = 0 \): \[ x^2 = 3 \] \[ x = \pm \sqrt{3} \] Thus, the real solutions are: \[ x = 0, \quad x = \sqrt{3}, \quad x = -\sqrt{3} \]