Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = -2x^4 + 4x^3 + 3x^2 + 18

Answer 1

`\text{Possible rational zeros}=\pm1,\pm(1)/(2),\pm2,\pm3,\pm(3)/(2),\pm6,\pm9,\pm(9)/(2),\pm18`

Explanation:

We have been given the function

`f(x)=-2x^2+4x^3+3x^2+18`

From the rational zeros theorem, we have

`\text{Possible rational zeros}=\pm\frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}`

From the given function,

Leading coefficient = 2

Factors of 2 are 1,2

Constant term = 18

Factors of constant term = 1, 2, 3, 6, 9, 18

Hence, we have

`\text{Possible rational zeros}=\pm(1,2,3,6,9,18)/(1,2)\\\\\text{Possible rational zeros}=\pm1,\pm(1)/(2),\pm2,\pm3,\pm(3)/(2),\pm6,\pm9,\pm(9)/(2),\pm18`