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

Two rational solutions

One rational solution

Two irrational solutions

Two complex solutions

Trinomial 2x² + 4x + 4.

It's of the form ax²+bx+c and it's discriminant is Δ=b² - 4. a. c

(in our case Δ = 4² - (4) (2) (4) → Δ = - 32

We know that: x' = - 1 + i and x" = - 1 - i

If Δ > 0 we have 2 rational solutions x' and x"

If Δ = 0 we have1 rational solution x' = x"

If Δ < 0 we have 2 complex solutions x' and x", that are conjugate

In our example we have Δ = - 16 then <0 so we have 2 complex solutions

That are x' = [-b+√Δ]/2. a and x" = [-b-√Δ]/2. a

x' =