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' =