the Given:
The given equation is,
[tex]f(x)=6x^3-2x^2+x+3[/tex]
The objective is to select the zeroes of the expression using the Rational Zero Theorem.
Explanation:
The general formula to calculate the zeroes using Rational Zero Theorem is,
[tex]\frac{p}{q}=\frac{factors\text{ of last term}}{factors\text{ of coefficient of highest degre}e}[/tex]
To find factors of the last term:
The end term of the function is 3. Then, the factors of the value 3 are,
[tex]Factors\text{ of 3 = }\pm1,\pm3[/tex]
To find factors of coefficient the highest degree:
The highest degree in the function is 3. The coefficient value of the highest degree is 6.
Then, the factors of 6 are,
[tex]\text{Factors of 6 = }\pm1,\text{ }\pm2,\text{ }\pm3,\text{ }\pm6[/tex]
To find ratios:
Then, the ratios can be written as,
[tex]\frac{p}{q}=\pm\frac{1}{1},\pm\frac{1}{2},\pm\frac{1}{3},\pm\frac{1}{6},\pm\frac{3}{1},\pm\frac{3}{2},\pm\frac{3}{3},\pm\frac{3}{6}[/tex]
The zeroes given in the options are -3 and 3/2.
Hence, options (A) and (C) are the correct answers.
