Question

How many solutions does the following equation have?

Answer 1

All quadratic equations have 2 roots; they can be 2 real, different ones, or 2 real, identical ones, or 2 imaginary ones or 2 complex ones.  You can tell immediatey from the discriminant b^2-4a(c):

If the D is +, you'll have 2 real, unequal roots;
If              0, you'll have 2 real, equal roots;
If the D is -, you'll have 2 complex or imaginary roots, different


Here a=2, b= -3 and c =5, so the discrim. is (-3)^2 - 4(2)(5) = 9-40 = -36.
Because the discrim. is -, you'll have 2 complex roots.