Question

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?

Answer 1

7/3 is the answer to your question

Answer 2

All the potential root of f(x) are
`\pm 1,\pm7, \pm (1)/(3),\pm (7)/(3), \pm (1)/(9),\pm (7)/(9)`.

Explanation:

According to the rational root theorem, all the potential root of f(x) are defined as

`x=\pm(p)/(q)`

Where, p is factor of constant term and q is factor of leading coefficient.

The given function is

`f(x)=9x^8+9x^6-12x+7`

Here, constant term is 7 and leading coefficient is 9.

Factors of 7 are ±1, ±7 and the factors of 9 are ±1, ±3, ±9.

Using rational root theorem, all the potential root of f(x) are

`x=\pm 1,\pm7, \pm (1)/(3),\pm (7)/(3), \pm (1)/(9),\pm (7)/(9)`

Therefore all the potential root of f(x) are
`\pm 1,\pm7, \pm (1)/(3),\pm (7)/(3), \pm (1)/(9),\pm (7)/(9)`.