1.8.A.1Concept
The real zeros of a rational function correspond to the real zeros of the numerator for such values in its domain.
ExampleZeros from a factored numerator1 / 5
Find the real zeros of r(x) = (x − 2)(x + 3)/(x − 4).
| x | 2 | −3 | 4 |
| N(x) = (x − 2)(x + 3) | 0 | 0 | 14 |
| D(x) = x − 4 | −2 | −7 | 0 |
| r(x) | 0 | 0 | undefined |
Try it on paper first, then reveal each step to check your work.
Step 1 — Set the numerator equal to 0
(x − 2)(x + 3) = 0, so x = 2 or x = −3.