Question

Use the Rational Zero Theorem to select the values that are possible zeroes of the function, f(x) = 6x^3-2x^2+x+3. Select all the apply 2 answers

Answer 1

the Given:

The given equation is,

`f(x)=6x^3-2x^2+x+3`

The objective is to select the zeroes of the expression using the Rational Zero Theorem.

Step-by-step explanation:

The general formula to calculate the zeroes using Rational Zero Theorem is,

`(p)/(q)=\frac{factors\text{ of last term}}{factors\text{ of coefficient of highest degre}e}`

To find factors of the last term:

The end term of the function is 3. Then, the factors of the value 3 are,

`Factors\text{ of 3 = }\pm1,\pm3`

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,

`\text{Factors of 6 = }\pm1,\text{ }\pm2,\text{ }\pm3,\text{ }\pm6`

To find ratios:

Then, the ratios can be written as,

`(p)/(q)=\pm(1)/(1),\pm(1)/(2),\pm(1)/(3),\pm(1)/(6),\pm(3)/(1),\pm(3)/(2),\pm(3)/(3),\pm(3)/(6)`

The zeroes given in the options are -3 and 3/2.

Hence, options (A) and (C) are the correct answers.