video explanation

text explanation

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

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.