Determine k so that the following has exactly one real solut

Determine k so that the following has exactly one real solution. (Enter only the positive answer.) Preview

1) 2x^2 +kx +12 =0

to be a perfect square : b^2 -4ac =0

so, k^2 - 4*2*12 =0

k^2 = 96

k = sqrt96

2) x = (-1 +/- 3i)/2

So, 2x = -1 +/- 3i

(2x +1) = +/-3i

squaring both sides:

(2x+1)^2 = -(3)^2

4x^2 +1 +4x = -9 ( we know i^2 = -1)

4x^2 +4x +10 =0

3) eqution which has solution y = -3 and y = 6

(y +3)(y+6) =0

expanding the bracket : y^2 + 9y +18 =0