What is the discriminant of #x^2 + 5x + 7 = 0# and what does that mean?

1 Answer
Jul 27, 2015

Answer:

The discriminant is #-3#, which means there are two complex roots.

Explanation:

#x^2+5x+7=0# is a quadratic equation. The general form of a quadratic equation is #a^2+bx+c#, where #a=1, b=5, and c=7#.
The discriminant, #"D"#, comes from the quadratic formula in which #x=(-b+-sqrt(color(red)(b^2-4ac)))/(2a)# .

#"D"=b^2-4ac# =

#"D"=5^2-4(1)(7)# =

#"D"=25-28# =

#"D"=-3#

A negative discriminant means there are two complex roots (x-intercepts).