Given the trinomial 2x^2 + 4x + 4 predict the type of solutions

The roots can be identified using the quadratic formula, specifically the discriminant. 

To get the dicriminant of the quadratic,  ax² + bx + c, we use: 
D = b² - 4ac 

If D ≥ 0,  two real valued roots. 
If D = 0,  two real, rational, unequall roots
If D > 0 (perfect square) two real, rational, and unequal roots.
If D > 0 (non-perfect square) there are two real,  irrational, and unequal roots. 
if D < 0, two complex valued solutions (forms complex conjugate pair)

So for the quadratic 2x² + 4x + 4: 
D =b² - 4ac = 4² - 4(2)(4) = 16 -32 = -16 

D< 0  the roots can be two complex roots.or a conjugate pair of complex roots.