Question

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

Answer 1

ANSWER

The possible rational zeros are,


`\pm1,\pm2, \pm3,\pm6,\pm9,\pm18`



Step-by-step explanation

According to the rational roots theorem, the possible rational zeros of the polynomial


`p(x) = {x}^(4) + 2 {x}^(3) - 3 {x}^(2) - 4x + 18`

are all the possible factors of the constant term

`18`
expressed over all the possible factors of the highest degree of the polynomial which is 1 in the simplest form.


Therefore the possible rational zeros of the given polynomial function are,



`\pm1,\pm2, \pm3,\pm6,\pm9,\pm18`

Answer 2

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.