Given the equation x^2+4mx+(2m+1)^2=0 has no roots. Find the range of values of m.

Question

b^2-4ac=(4m^2)-4(1) (2m+1)

Answer 1

well, no real roots means that the discriminant is negative. So you need

(4m)^2-4(1)(2m+1) < 0
16m^2-8m-4 < 0
4m^2-2m-1 < 0

The roots of that quadratic are (1±√5)/4

So, the discriminant is negative when (1-√5)/4 < m < (1+√5)/4