Find all possible rational roots and all rational roots of P(x) = 4x3 - 15x2 - 31x + 30
| Find all possible rational zeros - rational numbers are ratio of integers i.e. -2/1 = -2, 0, 1/2, -3/2 | |
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Solve |
Step |
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p = ± 1, ±
2, ±
3, ± 5, ±
6, ±
10, ±
15, ±
30
q ± 1, ± 2, ± 4 |
p/q
where p are factors of the last coefficient 30. q are the factors of the first
coefficient 4.
Recall p/1 = p |
| where q = 2 | get rid of repeats |
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| where q = 4 | get rid of repeats |
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| All possible rational zeros - Final list- whooa!! | |
| ± 1, ± 2, ± 3, ± 5, ± 6, ± 10, ± 15, ± 30 and |  |
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Try the easy ones first. |
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| Start with -2 (I tried others first but they failed - You can use Descartes' Rules of Signs to narrow the search.) | |
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Q(x) =
4x2 -
23x +
15 = 0 x = 3/4 or x = 5 |
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There are three zeros for P(x) are{ -2, 3/4, 5} |
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Side note: P(x) = 4x3 - 15x2 - 31x + 30 = (x + 2)(4x - 3)(x - 5) |
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