This question wants us to solve for k the equation 6k^{2} + k = 2 which is a quadratic equation as it can be written as

6k^{2} + k − 2 = 0

A straightforward way to solve problems like this is to use the quadratic formula

where, in this problem,

a = 6, b = 1, and c = −2

Substituting we get

This gives

or

which is rejected as k>0.

Thus the correct answer is .

Note: A different and maybe quicker approach would be to start plugging in numbers and see which one satisfies the equation. We note that the left-hand side of the equation involves 6 times the square of a number plus this number and the right-hand side the relatively “small” integer 2. So, we can assume that possibly the integers 2 and 3 in the options won’t work as they will give too big numbers on the left-hand side of the equation. Therefore, we try fractions in the options and find out that works.

Related Lessons

Watch the lessons below for more detailed explanations of the concepts tested in this question.
And don't worry, you'll be able to return to this answer from the lesson page.