SOLUTION: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rationa

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Question 246910: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
t2 + 4t + 4 = 0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
t2 + 4t + 4 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A4=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%284%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B4x%2B4+=+1%28x--2%29%2A%28x--2%29

Again, the answer is: -2, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B4+%29