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o-na [289]
3 years ago
7

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

Mathematics
1 answer:
marishachu [46]3 years ago
6 0

Answer:

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

Step-by-step 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\frac{1,2,3,6,9,18}{1,2}\\\\\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18

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