Question

Use the rational zero theorem to create a list of all possible rational zeroes of the function f(x) = 14x^7 - 4x^2 + 2

Answer 1

$f(x) = 14x^7 - 4x^2 + 2$

Use the rational zero theorem

In rational zero theorem, the rational zeros of the form +-p/q

where p is the factors of constant

and q is the factors of leading coefficient

$f(x) = 14x^7 - 4x^2 + 2$

In our f(x), constant is 2 and leading coefficient is 14

Factors of 2  are 1, 2

Factors of 14  are 1,2, 7, 14

Rational zeros of the form +-p/q  are

$+-\frac{1,2}{1,2,7,14}$

Now we separate the factors

$+-\frac{1}{1}, +-\frac{1}{2}, +-\frac{1}{7}, +-\frac{1}{14},+-\frac{2}{1}, +-\frac{2}{2}, +-\frac{2}{7}, +-\frac{2}{14}$

$+-1, +-\frac{1}{2}, +-\frac{1}{7}, +-\frac{1}{14},+-2, +-1 , +-\frac{2}{7}, +-\frac{1}{2}$

We ignore the zeros that are repeating

$+-1, +-2, +-\frac{1}{2}, +-\frac{1}{7}, +-\frac{1}{14}, +-\frac{2}{7}$

Option A is correct

Answer 2

Answer:

$\pm 1, \pm 2 \pm \frac{1}{2},\pm \frac{1}{7},\pm \frac{1}{14}, \pm \frac{2}{7}$

Step-by-step explanation:

By the rational root theorem or rational zero theorem,

The possible;e solutions of a polynomial function is,

$\pm(\frac{\text{factors of the constant term}}{\text{Factors of the leading coefficient}})$

Here, the given function,

$f(x) = 14x^7 - 4x^2 + 2$

Constant term = 2 and Leading coefficient = 14,

Factors of 2 = 1, 2,

Factors of 14 = 1, 2, 7, 14

Hence, the possible roots of the function,

$\pm(\frac{1, 2}{1, 2, 7, 14})$

$=\pm 1, \pm 2, \pm \frac{1}{2},\pm \frac{1}{7},\pm \frac{1}{14},\pm \frac{2}{7}$