Find the roots/solutions/zeroes: 2

82.    We have a "double-root" of  x = -5

Whenever the graph just touches the x axis like this....the discriminant will be 0

83. Soutions = Roots.....they are x = 1   and x = 5

When the graph passes through the x axis like this....the discriminant is > 0

84. Note that the graph has no real zeroes

I believe the the function shown is   y = (x - 1)^2 + 1

So...setting this to 0, we have that

(x - 1)^2 + 1  = 0

(x - 1)^2   = -1       take both roots

x - 1  =  ±√-1

x - 1 =  ±i

x =  1 ± i      = the zeroes

When we have non-real roots.....the discriminant is < 0