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.
