10. Roots and Zeros
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Construct a table to find all of the possible values of the expression for each of the values from the replacement set.
± 1, ± 7, ± 1/2, ± 7/2, ± 1/3, ± 7/3, ± 1/6, ± 7/6
To find all of the possible values of ± ba, replace both variables with each value from the replacement sets and simplify the expression.
| ± | a | b | ±b/a | Simplify |
|---|---|---|---|---|
| + | 1 | 1 | +1/1 | 1 |
| - | 1 | 1 | -1/1 | -1 |
| + | 1 | 7 | +7/1 | 7 |
| - | 1 | 7 | -7/1 | -7 |
| + | 2 | 1 | +1/2 | 1/2 |
| - | 2 | 1 | -1/2 | -1/2 |
| + | 2 | 7 | +7/2 | 7/2 |
| - | 2 | 7 | -7/2 | -7/2 |
| + | 3 | 1 | +1/3 | 1/3 |
| - | 3 | 1 | -1/3 | -1/3 |
| + | 3 | 7 | +7/3 | 7/3 |
| - | 3 | 7 | -7/3 | -7/3 |
| + | 6 | 1 | +1/6 | 1/6 |
| - | 6 | 1 | -1/6 | -1/6 |
| + | 6 | 7 | +7/6 | 7/6 |
| - | 6 | 7 | -7/6 | -7/6 |
We can now write all of the possible values of ± ba. ± 1, ± 7, ± 1/2, ± 7/2, ± 1/3, ± 7/3, ± 1/6, ± 7/6