Answer:
[tex]\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18[/tex]
Step-by-step explanation:
We have been given the function
[tex]f(x)=-2x^2+4x^3+3x^2+18[/tex]
From the rational zeros theorem, we have
[tex]\text{Possible rational zeros}=\pm\frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}[/tex]
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
[tex]\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[/tex]
