SOLUTION: 5a. (i) How many solutions exist for a quadratic equation? Explain. (ii) How do we determine whether the solutions are real or complex? I have no idea how to approach e

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Question 182673: 5a.

(i) How many solutions exist for a quadratic equation? Explain.
(ii) How do we determine whether the solutions are real or complex?

I have no idea how to approach either of these. thanks for the help.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
This is well covered by the onsite solver.
As an example
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=49 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, -4. Here's your graph:

Example 2

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 : .

The discriminant -15 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -15 is + or - .

The solution is , or
Here's your graph:

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