Math

The Quadratic Formula

Another method to solve a quadratic equation is using the quadratic formula. For a quadratic equation of the form:

The quadratic formula is given by:

                                                                                   

The number of solutions of a quadratic equation depends on the radical term in the quadratic formula. There are three cases for the solutions of a quadratic equation:

Case 1) , the equation has two solutions.

Case 2) , the equation has one solution.

Case 3) , the equation has no real solutions.

Example: Solve  using the quadratic formula.

We identify the following coefficients:

We now have to substitute the above values into the quadratic formula and simplify:

Example: Solve  using the quadratic formula.

We identify the coefficients in the quadratic equation:

Using the quadratic formula we get:

Example: Solve  using the quadratic formula. 

We have the following coefficients:

now, we put the above values in the quadratic formula:

since there is a negative number under the square root, the equation has no real solutions.