How do you find the discriminant and how many solutions does #y= x^2 + 3x# have?

1 Answer
May 8, 2015

The discriminant of an expression #ax^2+bx+c# is
#Delta = b^2-4ac#
(extracted from the quadratic formula for solutions
#x= (-b+-sqrt(Delta))/(2a)#

Extend the quadratic in the given equation so it looks like the general form:
#y = (1)x^2 +3x +0#

#Delta = 3^2-4(1)(0) = 9#

If you look back to the quadratic formula you can see:

#Delta {(<0 rarr "no Real solutions"),(=0 rarr "exactly 1 solution"), (>0 rarr "2 solutions") :}#

In our case #Delta>0#
so #y=x^2+3x# has 2 solutions