You can help keep this site free, by visiting our sponsor, Algebrator - an incredible software program that provides step - by - step solution to not only equations but to any other algebra problem as well!
home
solving equations with fractions
methods for solving quadratic equations
solving equations
solving equations
linear equations
solving equations
solving equations with variables on each side
solving equations
linear equations
solving linear equations
steps for solving linear equations
solving equations with variables on each side
solving quadratic equations
solving equations
solving equations
steps for solving linear equations
quadratic equations
writing linear equations
solving equations
solving rational equations
solving equations
solving equations
solving systems of equations using elimination
solving linear equations
solving equations
solving quadratic equations
methods for solving quadratic equations
solving equations
solving equations
equation solving resources
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Using the Discriminant to predict the roots of a quadratic equation

The discriminant of a quadratic equation is the value under the square root sign in the quadratic formula.

Remember the quadratic formula for an equation in the form ax + bx + c = 0 is:

From this formula the discriminant is: b - 4ac

When you evaluate the discriminant for a quadratic equation, if the result is:

positive You will have 2 different real solutions to the equation
  If this number is a perfect square number, there will be 2 different rational answers. If this number is a not perfect square number, there will be 2 different irrational answers.
zero You will have 1 real, rational solution to the equation - that is, there will be a repeated answer
negative You will have no real solutions to the equation (only imaginary answers)

 

Examples:

Use the discriminant to predict the roots of the following equations:

1. x + 7x + 12 = 0 a = 1 b = 7 c = 12 b - 4ac = 7 - 4(1)(12) = 49 - 48 = 1

Since the result is positive, there should be 2 different real solutions.

In fact, there will be 2 different rational solutions because 1 is a perfect square number.

(Perfect square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, etc)

2. x + 7x + 3 = 0 a = 1 b = 7 c = 3 b - 4ac = 7 - 4(1)(3) = 49 - 12 = 37

Since the result is positive, there should be 2 different real solutions.

In fact, there will be 2 different irrational solutions because 37 is not a perfect square number.

3. x + 4x + 4 = 0 a = 1 b = 4 c = 4 b - 4ac = 4 - 4(1)(4) = 16 - 16 = 0

Since the result is zero, there should be only one real, rational solution

4. x - x + 4 = 0 a = 1 b = -1 c = 4 b - 4ac = (-1) - 4(1)(4) = 1 - 16 = -15

Since the result is negative, there should be no real solutions.