Answer:
The correct options are:
A. [tex]\pm 7[/tex]
B. [tex]\pm \dfrac{1}{2}[/tex]
D. [tex]\pm 1[/tex]
Step-by-step explanation:
Rational Root theorem--
For any polynomial function of the type:
[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+.............+a_1x+a_0[/tex] where [tex]a_i's[/tex] are integers.
The rational roots are of type p/q where p is the factor of [tex]a_0[/tex] and q is the factor of [tex]a_n[/tex]
- We have a polynomial function as:
[tex]f(x)=2x^2-3x+7[/tex]
Here p is a factor of 7.
i.e.p could take value 1,-1, 7 and -7.
and q is a factor of 2.
i.e. q could take value 1,-1,2 and -2.
The possible rational roots are given by:
[tex]\pm 7,\pm \dfrac{1}{2}\ and\ \pm 1[/tex]
