Any equation in the form
is said to be in
quadratic form. This equation can then be solved by using the quadratic formula, by completing the square, or by factoring if it is factorable.
Example 1: Solve
by (a) factoring and (b) applying the quadratic formula.
By the zero product rule,
is equivalent to
When applying the quadratic formula to equations in quadratic form, you are solving for the variable name of the middle term. Thus, in this case,
Using the square root property,
Example 2: Solve
by (a) factoring and (b) applying the quadratic formula.
In the last step on the right,
must be a nonnegative value; therefore,
has no solutions. The only solution is
.
When applying the quadratic formula to this quadratic form equation, you are solving for
There is no solution for
Thus,
is the only solution.
Linear Sentences in One Variable
Quadratics In One Variable
