Which of the following are possible rational roots of the polynomial function

The correct options are:

          A.  

          B.  

          D.  

Rational Root theorem--

For any polynomial function of the type:

where are integers.

The rational roots are of type p/q where p is the factor of and q is the factor of

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:

Let's simplify step-by-step To understand :)

3x2−7x−(x2+3x−9)

Distribute the Negative Sign:

=3x2−7x+−1(x2+3x−9)

=3x2+−7x+−1x2+−1(3x)+(−1)(−9)

=3x2+−7x+−x2+−3x+9

Combine Like Terms:)

=3x2+−7x+−x2+−3x+9

=(3x2+−x2)+(−7x+−3x)+(9)

=2x2+−10x+9

Answer :)

=2x2−10x+9

HOPE THIS HELPS