Problem: how do i solve f(x)= 2x to the 2nd power minus 2x + 1
its a parabolas problem
f(x) simply means "function of x." Treat the equation as
y = 2x^2 - 2x + 1 and try to solve for the values of x.
Unfortunately, this equation has no real roots. The parabola
doesn't cross the x-axis. The lowest point is at (0.5, 0.5).
In problems of this type, the discriminant is b² - 4*a*c
It will tell us whether there are two, one or no roots.
b² - 4*a*c
(-2)² - 4*2*1
4 - 8
-4
Because we need the square root of the discriminant, we
are asking for the square root of a negative number. The
answer to that is ±2i.
±2i
x = ------
2a
±2i
x = ------
2*2
±2i
x = ------
4
±i
x = ----
2
i -i
x = ---- and x = ----
2 2