To solve this problem, we make use of the discriminant. The discriminant is a value which reveals the type of solution or roots and equation has. It has the formula:
D = b^2 – 4 a c
where the coefficients are taken from the equation ax^2 + bx + c. The conditions are:
D < 0 no real roots = two roots that are complex conjugates
D = 0 one real zero
D > 0 two distinct real roots
Given the equation 2x^2 + 4x + 4, the coefficients are therefore:
a = 2
b = 4
c = 4
Plugging these values into the formula:
D = 4^2 – 4 (2) (4)
D = -16
Therefore the solutions or the roots are complex conjugates or imaginary. Hence there is no real root.