SOLUTION: Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation. y = x^2 + 8x + 16

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Question 172247This question is from textbook Introductory Algebra
: Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation.
y = x^2 + 8x + 16 This question is from textbook Introductory Algebra

Found 2 solutions by nerdybill, KnightOwlTutor:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
For:
y = x^2 + 8x + 16
a = 1
b = 8
c = 16
.
discriminant b^2 - 4ac
= 8^2 - 4(1)(16)
= 64 - 64
= 0
.
Since discriminant = 0, there is only "one real solution".

Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B16+=+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=%288%29%5E2-4%2A1%2A16=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%288%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B8x%2B16+=+1%28x--4%29%2A%28x--4%29

Again, the answer is: -4, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B16+%29