Quadratic Formula Discriminant

This section has the following videos:

  • Lesson Video
  • Example Set A Practice Problems (Video Solutions)
  • Example Set B Practice Problems (Video Solutions)
  • Example Set C Practice Problems (Video Solutions)

A very interesting part of the quadratic formula is the discriminant.  Specifically the discriminant is the “b squared – 4ac” part of the formula (located under the square root symbol).  This part of the quadratic formula can tell us some useful information about the solutions of the equation.  Remember a quadratic equation will always have two solutions- simple enough concept to understand.  However where things get a little more interesting is understanding the type of solutions.  Quadratic equations can have real solutions(positive and negative numbers) or imaginary solutions(complex numbers).  Go get your calculator so I can show you the difference between real and imaginary numbers.  Use your calculator to find the square root of 16, no problem your calculator returned 4 because 4 x 4 = 16.  Now lets try to find the square root of -16 (negative 16), did your calculator start to smoke?  No, but it probably returned an error message on the screen. Why? because your calculator does not know a real number answer to the request “square root of -16.”   Let’s think about in terms of real numbers,  -4 x -4 = 16 , so if the square root of -16 is not -4 or 4 then what is the solution?  The square root of  -16 turns out to be a  special type of number called an imaginary number. As I said a quadratic equation can have real number solutions or imaginary number solution.   If the value of the discriminant is positive the quadratic equation has two real number roots, if the value is negative the equation has two imaginary roots and if the value is zero it have one double root( example x=2  and x=2 ).  As your study of algebra becomes more advance you will appreciate the little role the discriminant plays in the quadratic formula.