Question

According to the rational root theron what are all the potential roots of f(x)=9x^4-2x^2-3x+4

Answer 1

Potential roots:
`(9)/(4),(9)/(2),9,(3)/(4),(3)/(2),3, (1)/(4),(1)/(2),1`

Explanation:

Simply put, the rational roots theorem tells us that if there are any rational roots of a polynomial function, they must be in the form

±
`(FactorsOfa_(0))/(FactorsOfa_n)`

Where

a_n is the number before the highest power of the polynomial, and

a_0 is the constant in the polynomial

From the polynomial shown, we have a_n = 9 and a_0 = 4

The factors of 9 are 9, 3, 1

and

The factors of 4 are 4,2,1

So, if there are any rational roots, they would be:

±
`(FactorsOfa_(0))/(FactorsOfa_n)`

±
`(9,3,1)/(4,2,1)`

Which is ± 9/4, 9/2, 9/1, 3/4, 3/2, 3/1, 1/4, 1/2, 1/1

or

`(9)/(4),(9)/(2),9,(3)/(4),(3)/(2),3, (1)/(4),(1)/(2),1`