What are all values of for which ?

### Select an Answer

or

### View Correct Answer

The correct answer is C.

One way to determine all values of for which is first to rewrite the inequality in an equivalent form that compares a factored expression to and then reason about the arithmetic sign of the product of the factors. The inequality is equivalent to , which in turn is equivalent to . Since factors as , the original inequality is equivalent to or . To solve , notice that this inequality is satisfied by a value of precisely when either , or the product of the factors and is negative; this last condition is true for , as shown in the table below:

Therefore, all values of for which are described by the extended inequality .

Alternatively, one can use a graphing calculator. Graph the two equations and .

The values of for which are the same as the values of for which the parabolic graph of lies above or intersects the line . Therefore, all values of for which are described by the extended inequality .