Question

List the potential rational zeros of the polynomial function. Do not find the zeros.f(x) = -4x^4 + 2x^2 - 3x + 6A± , ± , ± , ± , ± 1, ± 2, ± 3, ± 4, ± 6B± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6C± , ± , ± , ± , ± , ± 1, ± 2, ± 4D± , ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6

Answer 1

±1,±2,±3 and ±6

Step-by-step explanation:

We make use of the Rational Zero theorem below:

If a polynomial has integer coefficients, then every rational zero of f(x) has the form p/q where p is a factor of the constant term ​and q is a factor of the leading coefficient.

Given the function:

`f\mleft(x\mright)=-4x^4+2x^2-3x+6`

The steps to follow are given below.

Step 1: Determine all factors of the constant term and all factors of the leading coefficient.

The constant term is 6: Factors are ±1,±2,±3 and ±6

The leading coefficient is -4: Factors are ±1,±2, and ±4.

Step 2: Determine all possible values of p/q.

`\begin{gathered} (p)/(q)=\pm(1)/(1),\pm(2)/(1),\pm(2)/(2),\pm(3)/(1),\pm(6)/(1),\pm(6)/(2) \\ =\pm1,\pm2,\pm1,\pm3,\pm6,\pm3 \\ =\pm1,\pm2,\pm3,\pm6 \end{gathered}`

Therefore, the potential zeros are: ±1,±2,±3 and ±6.