Given the trinomial 2x2 + 4x + 4, predict the type of solutions

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.