Solving Quadratic Equations by Using the Quadratic Formula
The Quadratic Formula The solutions of a
quadratic equation in the form ax^{ 2} + bx + c = 0,
where a0, are given by the formula .
Note that this formula can be used to find the solutions to any
quadratic equation.
Example 1
Solve x^{ 2} + x  2 = 0 by using the Quadratic
Formula.
Solution
In this equation, a = 1, b = 1, and c = 2.
Note that the discriminant b^{ 2}  4ac = 9. Since
this is greater than zero, we expect two solutions. Indeed, the
Quadratic Formula says that there are two solutions.
Check these solutions by factoring and graphing.
x^{ 2} + x  2 = (x  1)(x + 2)
x  1 = 0 or x + 2 = 0
x = 1 or x = 2
Example 2
Solve x^{ 2 } 2x + 2 = 0 by using que Quadratic
Formula.
Solution
In this equation the a = 1, b = 2 and c = 2.
So the solutions are and These numbers are
approximately  2.732 and 0.732. Notice that we could not have
solved this equation by factoring, since the function y = x^{
2 } 2x + 2 does not have integer roots.
