2x^2 - 5x + 7 = 0.

Find the discriminant.

Describe the roots and explain your reasoning.

The discriminant of

ax^2+b+c=0 is

b^2-4ac

when the discriminant is

less than 0, then there are no real roots

equal to 0, then there is 1 real root

greater than 0, then there are 2 real roots

so

2x^2-5x+7=0

a=2

b=-5

c=7

discriminat = (-5) ^2-4 (2) (7) = 25-28=-3

-3<0

no real roots