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
Solve x 2 + x - 2 = 0 by using the Quadratic
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
Solve -x 2 - 2x + 2 = 0 by using que Quadratic
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.