SOLUTION: What is a sign of D mena and discriminant mean and how does an example of an equation look?

Question 203987: What is a sign of D mena and discriminant mean and how does an example of an equation look?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What is a sign of D mena and discriminant mean and how does an example of an equation look
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This is covered well by the onsite solver.
EG: x^2 - x - 2 = 0

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=9 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2, -1. Here's your graph:

EG: x^2 - x + 2 = 0

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 -7 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 -7 is + or - .

The solution is , or
Here's your graph:

EG: x^2 - 6x + 9 = 0

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=0 is zero! That means that there is only one solution: .
Expression can be factored:

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

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