Find the discriminant of 3p^2-6p+8=0 and give the number and type of solutions to the equation

3p^2-6p+8=0 is in the form ap^2+bp+c = 0

we can see that
a = 3
b = -6
c = 8

The discriminant D is
D = b^2 - 4ac
D = (-6)^2 - 4*3*8
D = 36 - 96
D = -60

The discriminant is -60.

Since the discriminant is negative, this means that we have two non-real solutions (they are imaginary or complex solutions). If you graphed y = 3x^2-6x+8, you would find that there are no x intercepts. This parabola is completely above the x axis and never crosses or touches it.