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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.