SOLUTION: How would you solve problems like: x^2+5=0 x^2-11=0 Why is there two solutions? Thank you

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Question 194972: How would you solve problems like:
x^2+5=0
x^2-11=0
Why is there two solutions?
Thank you
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
How would you solve problems like:
x^2+5=0
x^2-11=0
Why is there two solutions?
----------------------
x^2+5=0
Since there's no x term:

x = ± i*sqrt(5) where i = sqrt(-1)
---------------------------------
x^2-11=0

x = +sqrt(11)
x = -sqrt(11)
-----------------
There are 2 solutions because both work.
In the 2nd eqn, both +sqrt(11) and -sqrt(11) are 11 when they're multiplied by themselves.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=44 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.3166247903554, -3.3166247903554. Here's your graph:

-------
If you graph them, you'll see that they cross the x-axis in 2 places (the 2nd one).
You can get FREE software to graph these at
www.padowan.dk.com/graph/
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