Find all the values of m for which the equation m(x)^2 + 3x + 1 − m = 0 has no real solutions.
This will have no real solutions when the discriminant is < 0
So
(3)^2 - 4(m) (1 - m) < 0
9 - 4m + 4m^2 < 0
4m^2 - 4m + 9 < 0
Looking at the graph here and subbing x for m,note that this function is always > 0
https://www.desmos.com/calculator/q6jmvmvy7y
So....no values of m give non-real solutions