# 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

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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?

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: