This question wants us to solve for k the equation 6k2 + k = 2 which is a quadratic equation as it can be written as
6k2 + 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
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.
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