Question

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

Two rational solutions
One rational solution
Two irrational solutions
Two complex solutions

Answer 1

i found out the solution is 2(x2+2x+2)

Answer 2

\(\color{#000000 }{ \displaystyle x^2+2x+1=(x+1)^2 }\) (Right ?)

\(\color{#000000 }{ \displaystyle 2x^2+4x+4=0 }\)
\(\color{#000000 }{ \displaystyle x^2+2x+2=0 }\) (divided each term by 2)
\(\color{#000000 }{ \displaystyle (x^2+2x+1)+1=0 }\)
\(\color{#000000 }{ \displaystyle (x^2+2x+1)=-1 }\)

Answer 3

What I am showing is called "completing the square [method]".
If you need an example of that method, let me know....

Answer 4

But im not sure of the answer choices, i was thinking "D" however it concludes in ONE solution

Answer 5

I wanted you to find the two solutions and then for you to choose the answer....


I will give you a hint for the answer after/by proceeding
\(\color{#000000 }{ \displaystyle x^2+2x+1=-1 }\)
\(\color{#000000 }{ \displaystyle (x+1)^2=-1 }\)
\(\color{#000000 }{ \displaystyle \sqrt{(x+1)^2}=\sqrt{-1} }\)

Answer 6

from there you should tell me what kind of answers/solutions you will get

Answer 7

im not sure what each one means

Answer 8

Im stuck between D and C though, the other ones dont seem logical to me

Answer 9

irrational number is [the result from] any Nth root of a non-perfect Nth.
(short but perhaps abstruse definition)

Also, irrational numbers include \(\pi\), \(e\), and others such...

Answer 10

So it eliminates answer choice A and B

Answer 11

Complex = Imaginary
Irrational = Real numbers that are 'approximate'

Answer 12

Leaving answer choice D, because -1 is equal to "i" (imaginary)