y=2x²+4x+1

The equation represents a parabola. To find the roots, set y=0: 2x²+4x+1=0. Use the quadratic formula x = [-b ± sqrt(b²-4ac)] / 2a. Here a=2, b=4, c=1. x = [-4 ± sqrt(4²-4*2*1)] / (2*2) = [-4 ± sqrt(16-8)] / 4 = [-4 ± sqrt(8)] / 4 = [-4 ± 2*sqrt(2)] / 4 = -1 ± sqrt(2)/2.