Question

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 – 6x8 + x3 – 4x + 3?

Answer 1

The possible potential root of 5x^{11} – 6x^8 + x^3 – 4x + 3 are

p's possible values are 1 and 3
q's possible values are 1 3 5 and 15
hope it helps

Answer 2

we have

`f(x) = 15x^(11) -6x^(8) + x^(3) - 4x + 3`

we know that

The Rational Root Theorem states that when a root 'x' is written as a fraction in lowest terms

`x=(p)/(q)`

p is an integer factor of the constant term, and q is an integer factor of the coefficient of the first monomial.

So

in this problem

the constant term is equal to
`3`

and the first monomial is equal to
`15x^(11)` -----> coefficient is
`15`

So

possible values of p are
`1, and\ 3`

possible values of q are
`1, 3, 5, and\ 15`

therefore

the answer is

The all potential rational roots of f(x) are

(+/-)
`(1)/(15)`,(+/-)
`(1)/(5)`,(+/-)
`(1)/(3)`,(+/-)
`(3)/(5)`,(+/-)
`1`,(+/-)
`3`