ANSWER
None of the above
EXPLANATION
The quadratic expression given to us is
[tex]6 {x}^{2} + 2x - 21[/tex]
If the discriminant of this quadratic expression is a perfect square, then it has rational factors,
If we compare the above expression to the general quadratic expression,
[tex]a {x}^{2} + bx + c[/tex]
We have,
[tex]a=6,b=2,c=-21[/tex]
The discriminant is given by,
[tex] D = {b}^{2} - 4ac[/tex]
Thus
[tex] D = {2}^{2} - 4(6)( - 21)[/tex]
[tex] D = 4 + 504 = 508[/tex]
Since 508 is not a perfect square, the expression
[tex]6 {x}^{2} + 2x - 21[/tex]
has no rational factors.
Therefore D is the correct answer.
