Algebra
QUADRATIC EQUATIONS
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
quadratic equation.
(2-8)
x
b ± b2
4ac
2a
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 =
and
b
b2
4ac
2a
x =
. The Quadratic Formula should be committed to memory because it is
b
b2
4ac
2a
such a useful tool for solving quadratic equations.
There are three steps in solving a quadratic equation using the Quadratic Formula.
Step 1.
Write the equation in general form.
Step 2.
Substitute the values for a, b, and c into the Quadratic Formula and solve
for x.
Step 3.
Check the roots in the original equation.
Rev. 0
Page 25
MA-02
