Question

Which of the following is a factor of 6x2 + 2x − 21?

Answer 1

ANSWER

None of the above

EXPLANATION

The quadratic expression given to us is

$6 {x}^{2} + 2x - 21$

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,

$a {x}^{2} + bx + c$
We have,
$a=6,b=2,c=-21$


The discriminant is given by,

$D = {b}^{2} - 4ac$

Thus

$D = {2}^{2} - 4(6)( - 21)$


$D = 4 + 504 = 508$

Since 508 is not a perfect square, the expression


$6 {x}^{2} + 2x - 21$
has no rational factors.


Therefore D is the correct answer.