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15 Solving Quadratic Equations
Quadratic equations in the variable x can always be put in the standard form
ax^2 ++bxbx c= 000 ,.aaa≠ 0 This type of equation is always solvable for the vari-
able x, and each result is a root of the quadratic equation. In one instance
the solution will yield only complex number roots. This case will be singled
out in the discussion that follows. You will get a feel for the several ways of
solving quadratic equations by starting with simple equations and working
up to the most general equations. The discussion will be restricted to real
number solutions. When instructions are given to solve the system, then you
are to fi nd all real numbers x that will make the equation true. These values
(if any) are the real roots of the quadratic equation.Solving Quadratic Equations of the Form ax^2 + c = 0
Normally, the fi rst step in solving a quadratic equation is to put it in stan-
dard form. However, if there is no x term, that is, if the coeffi cient b is 0,
then you have a simple way to solve such quadratic equations.Problem Solve^2 =− 4.Solution
Step 1. Because the square of a real number is never negative, there is no
real number solution to the system.