Question

Use the rational zeroes theorem to state all the possible zeroes of the following polynomial:
f (x) = 3x^(6) + 4x^(3) - 2x^(2) + 4

Answer 1

Answer:

All the possible zeroes of the polynomial: f(x) = $3x^{6} + 4x^{3} - 2x^{2} +4$ are  ±1 , ±2 ,  ±4 ,  ±$\frac{1}{3}$ , ±$\frac{2}{3}$  , ±$\frac{4}{3}$ by using rational zeroes theorem.

Step-by-step explanation:

Rational zeroes theorem gives the possible roots of polynomial f(x) by taking ratio of p and q where p is a factor of constant term and q is a factor of the leading coefficient.

The polynomial f(x) = $3x^{6} + 4x^{3} - 2x^{2} +4$

Find all factors (p) of the constant term.

Here we are looking for the factors of 4, which are:

±1 , ±2 and ±4

Now find all factors (q) of the coefficient of the leading term

we are looking for the factors of 3, which are:

±1 and ±3

List all possible combinations of ± $\frac{p}{q}$  as the possible zeros of the polynomial.

Thus, we have ±1 , ±2 ,  ±4 ,  ±$\frac{1}{3}$ , ±$\frac{2}{3}$  , ±$\frac{4}{3}$ as the possible zeros of the polynomial

Simplify the list to remove and repeated elements.

All the possible zeroes of the polynomial: f(x) = $3x^{6} + 4x^{3} - 2x^{2} +4$ are  ±1 , ±2 ,  ±4 ,  ±$\frac{1}{3}$ , ±$\frac{2}{3}$  , ±$\frac{4}{3}$

Learn more about Rational zeroes theorem here -https://brainly.ph/question/24649641

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