#1**+1 **

1) D, This is the area outside a circle of radius 1 but inside the sort of rounded square of "radius" 1.

There is a continuum of points satisfying this.

2)

\(x^4-x^2+2x-1 = \\ x^4 - (x^2 - 2x+1) = \\ x^4 - (x-1)^2 = \\ (x^2 - (x-1))(x^2+(x-1)) = \\ (x^2 -x +1)(x^2+x-1)\\ \text{The discriminant of the first factor is } D=(-1)^2 -4 = -3\\ \text{The discriminant of the second factor is }D=1+4=5\\ \text{Thus the first factor has no real roots, while the second has two real roots}\\ \text{Thus there are a total of two real roots of the original equation}\)

Rom
Nov 10, 2018