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Artemon [7]
2 years ago
12

Use the rational zeroes theorem to state all the possible zeroes of the following polynomial:

Mathematics
1 answer:
Mkey [24]2 years ago
7 0

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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