This chapter covers solving for unknowns using quadratic equations.
APPLY the quadratic formula to solve for an unknown.
Types of Quadratic Equations
A quadratic equation is an equation containing the second power of an unknown but no higher
power. The equation x2 - 5x + 6 = 0 is a quadratic equation. A quadratic equation has two roots,
both of which satisfy the equation. The two roots of the quadratic equation x2 - 5x + 6 = 0 are
x = 2 and x = 3. Substituting either of these values for x in the equation makes it true.
The general form of a quadratic equation is the following:
ax2 - bx + c = 0
The a represents the numerical coefficient of x2 , b represents the numerical coefficient of x, and
c represents the constant numerical term. One or both of the last two numerical coefficients may
be zero. The numerical coefficient a cannot be zero. If b=0, then the quadratic equation is
termed a "pure" quadratic equation. If the equation contains both an x and x2 term, then it is a
"complete" quadratic equation. The numerical coefficient c may or may not be zero in a
complete quadratic equation. Thus, x2 + 5x + 6 = 0 and 2x2 - 5x = 0 are complete quadratic
Solving Quadratic Equations
The four axioms used in solving linear equations are also used in solving quadratic equations.
However, there are certain additional rules used when solving quadratic equations. There are
three different techniques used for solving quadratic equations: taking the square root, factoring,
and the Quadratic Formula. Of these three techniques, only the Quadratic Formula will solve all
quadratic equations. The other two techniques can be used only in certain cases. To determine
which technique can be used, the equation must be written in general form:
ax2 + bx + c = 0
If the equation is a pure quadratic equation, it can be solved by taking the square root. If the
numerical constant c is zero, equation 2-1 can be solved by factoring. Certain other equations
can also be solved by factoring.