SOLUTION: Is it possible for a quadratic equation to have 0 solutions? 1 solution? 2 solutions? More than 2 solutions? How can you tell algebraically AND graphically how many solutions a

Question 278943: Is it possible for a quadratic equation to have 0 solutions? 1 solution? 2 solutions? More than 2 solutions?
How can you tell algebraically AND graphically how many solutions a quadratic equation has?

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
graphically
if the parabola touches the x axis twice there are two solutions
if it touches once there is one solution
if it never touches the x axis there are no real solutions
algebraically
x^+4x+4=0
x^2-2x-3=0
x^2-2x+3=0
check out the determinants in these three equations

Solved by pluggable solver: SOLVE quadratic equation with variable

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: -2, -2. Here's your graph:

Solved by pluggable solver: SOLVE quadratic equation with variable

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=16 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -1. Here's your graph:

Solved by pluggable solver: SOLVE quadratic equation with variable

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 -8 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 -8 is + or - .

The solution is

Here's your graph:

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