TABLE OF CONTENTS We have seen how to solve linear equations, or equations of first degree, or degree 1, in which the highest exponent on the variable x is 1. Now we turn our attention to second degree equations, in which the highest exponent on the variable is 2, such as x 2. These equations of degree 2 are called quadratic equations.
The word quadratic contains the root word quadras, the Latin word for square.
Consider the following quadratic equations:
The first two equations can be easily solved by inspection. In the first equation, the obvious solution is x = 3, since 3 2 = 9. However, this is not a complete solution because x = ?3 also satisfies this equation since ( ?3) 2 = 9. In the second equation we can also find the solutions by simply examining the equation. We find that x = 1 and x = ?1 both satisfy the equation, because 1 2 ? 1 = 0, and ( ?1) 2 ? 1 = 0.
As was true in equations of degree 1, to solve a quadratic, we must isolate x. Again consider x 2 = 9. The x 2 stands alone; so to isolate x we need only take the square root of both sides of...
