Given:
The polynomial function is
[tex]F(x)=4x^3-6x^2+9x+10[/tex]
To find:
The possible roots of the given polynomial using rational root theorem.
Solution:
According to the rational root theorem, all the rational roots and in the form of [tex]\dfrac{p}{q}[/tex], where, p is a factor of constant and q is the factor of leading coefficient.
We have,
[tex]F(x)=4x^3-6x^2+9x+10[/tex]
Here, the constant term is 10 and the leading coefficient is 4.
Factors of constant term 10 are ±1, ±2, ±5, ±10.
Factors of leading term 4 are ±1, ±2, ±4.
Using rational root theorem, the possible rational roots are
[tex]x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}[/tex]
Therefore, the correct options are A, C, D, F.
