Write down the value of the largest integer, k ,so that the equation 3x + 2/x2 + 1 = k has exactly one solution.

Question

Write down the value of the largest integer, k ,so that the equation 3x + 2/x2 + 1 = k has exactly one solution.

 

How to find k?

Answer 1

(3x+2)/x^2 + 1 = k

 

(3x+2) + x^2 = kx^2

 

0 = kx^2 - x^2 - 3x - 2

 

0 = (k-1)x^2 - 3x - 2

 

The discrimminant must be zero so that there is 1 solution

 

0 = B^2 - 4AC = (-3)^2 - 4(k-1)(-2) = 9 + 8(k-1)

 

                                                       = 9 + 8k - 8

                                                       = 1 + 8k

 

K = -1/8