Your solution a = x = -1,1 are the points of intersection between the line and the parabola therefore they should then be put back into the function x^2+1 giving you two points (-1, 2) and (1,2)

The two tangent lines can now be found with

(-1, 2) and (0,0) gives y = -2x

then

(1, 2) and (0,0) gives y = 2x

Do you follow?