Question

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

A. 0
B. 1/7
C. 2 (It's not this one I tried)
D. 7/3

Answer 1

It is D. 7/3 because the rational root theorem states that when a root 'x' is written as a fraction x = p/q in lowest terms, p is an integer factor of the constant term (i.e. 7), and q is an integer factor of the coefficient of the first monomial (i.e. 9x^8).

Answer 2

`\boxed{\boxed{(7)/(3)}}`

Solution-

Rational Root Theorem-

`f(x)=a_nx^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+.......+a_1x+a_0\ \ \ and\ a_n\\eq 0`

All the potential rational roots are,

`=\pm (\frac{\text{factors of}\ a_0}{\text{factors of}\ a_n})`

The given polynomial is,

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

Here,

`a_n=9,\ a_0=7\\\\\text{factors of}\ 9=1,3,9\\\\\text{factors of}\ 7=1,7`

The potential rational roots are,

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

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

From, the given options only
`(7)/(3)` satisfies.