Use the discriminant to describe the roots of each equation. then select the best description. x2 - 5x + 7 = 0

The general form of a quadratic (second degree) equation is 

, where

is called the Discriminant.

The Discriminant determines how many roots the equation will have as follows:

i)  if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.

In our equation, , a=1, b=-5, c=7

so the discriminant is D=(-5)^2-4*1*7=25-28<0

Thus the equation has no roots.

Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.