The Quadratic Formula
Many quadratic equations cannot readily be solved by either of the two techniques already
described (taking the square roots or factoring). For example, the quadratic equation
x2 - 6x + 4 = 0 is not a pure quadratic and, therefore, cannot be solved by taking the square roots.
In addition, the left-hand side of the equation cannot readily be factored. The Quadratic Formula
is a third technique for solving quadratic equations. It can be used to find the roots of any
b ± b2
Equation 2-8 is the Quadratic Formula. It states that the two roots of a quadratic equation written
in general form, ax2 + bx + c = 0, are equal to x =
. The Quadratic Formula should be committed to memory because it is
such a useful tool for solving quadratic equations.
There are three steps in solving a quadratic equation using the Quadratic Formula.
Write the equation in general form.
Substitute the values for a, b, and c into the Quadratic Formula and solve
Check the roots in the original equation.