Openstudy what are the possible rational zeros of f (x) = x4 + 2x3 - 3x2 - 4x + 18? ± 1, ± 2, ± 3, ± 4, ± 5, ± 6, ± 7, ± 8, ± 9, ± 10, ± 11, ± 12, ± 13, ± 14, ± 15, ± 16, ± 17, ±18 ± 1, ± 2, ± 3, ± 6, ± 9, ± 18 1, 2, 3, 6, 9, 18 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

Question

Mathematics

Braeden Webb

4 November, 02:07

Openstudy what are the possible rational zeros of f (x) = x4 + 2x3 - 3x2 - 4x + 18? ± 1, ± 2, ± 3, ± 4, ± 5, ± 6, ± 7, ± 8, ± 9, ± 10, ± 11, ± 12, ± 13, ± 14, ± 15, ± 16, ± 17, ±18 ± 1, ± 2, ± 3, ± 6, ± 9, ± 18 1, 2, 3, 6, 9, 18 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

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Karina Chambers · Answer 1

We are given with the following equation as written below,

f (x) = x⁴ + 2x³ - 3x² - 4x + 18

The number of roots or solution of the equation is equal to 4. This is because the number of roots of the equation is equal to the degree. The roots could be real or imarginary. They could be rational or irrational. The possible rational zeroes of the equation are the positive and negative values of the constant term.

Our constant is 18. The factors of 18 are 1, 2, 4, 6, and 9, 18. Therefore, the possible values are + / - 1, + / - 2, + / - 4, + / - 6, + / - 9, + / - 18.