Answer:
Potential roots: [tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]
Step-by-step 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
± [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]
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:
± [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]
± [tex]\frac{9,3,1}{4,2,1}[/tex]
Which is ± 9/4, 9/2, 9/1, 3/4, 3/2, 3/1, 1/4, 1/2, 1/1
or
[tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]
