Question

Use the rational zero theorem to create a list of all possible rational zeroes of the function f(x) = 6x^4 - 3x^2 + 2

Answer 1

Answer:

B) +/- 1, +/-2, +/- $\frac{1}{3}$, +/-$\frac{1}{6}$, +/-$\frac{2}{3}$

Step-by-step explanation:

Definition of Rational Zero Theorem.

If P(x) is a polynomial with integer coefficients and if p/q is a zero of P(x) P(p/q) = 0), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

We are given the polynomial f(x) = 6x^4 - 3x^2 + 2

Here the constant term is 2 and the leading coefficient is 6.

Now find the factors of 2 and 6.

Factors of 2: 1, -1, 2, -2

Factors of 6: 1, -1, 2, -2, 3, -3, 6, -6

Possible values of p/q is

+/-1, +/-2, +/- 1/2, +/-1/3, +/- 1/6, +/-2/3

The answer is B) +/- 1, +/-2, +/- $\frac{1}{3}$, +/-$\frac{1}{6}$, +/-$\frac{2}{3}$

Thank you.