We can never multiply two numbers and obtain an answer of zero unless at least one of the numbers is zero.
Of course, both of the numbers can be zero since (0)(0) = 0. The solutions can be indicated either by writing x = 6 and x = - 1 or by using set notation and writing , which we read "the solution set for x is 6 and - 1." In this text we will use set notation.
An incomplete quadratic with the b term missing must be solved by another method, since factoring will be possible only in special cases.
Note that in this example we have the square of a number equal to a negative number.
For instance, note that the second form came from adding 7 to both sides of the equation.
Never add something to one side without adding the same thing to the other side.
We will solve the general quadratic equation by the method of completing the square.
Certain types of word problems can be solved by quadratic equations.
The process of outlining and setting up the problem is the same as taught in chapter 5, but with problems solved by quadratics you must be very careful to check the solutions in the problem itself.
The physical restrictions within the problem can eliminate one or both of the solutions.