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.