How to use the discriminant to find out what type of solutions the equation has for #x^2 - 8x + 3 = 0#?

1 Answer
May 23, 2015

For a quadratic of the form
#ax^2 +bx+c=0#
the discriminant is
#Delta = b^2-4ac#
where
#Delta { (<0 rarr "no Real solutions"),(=0 rarr "1 Real solution"),(>0 rarr "2 Real solutions"):}#

Given
#x^2-8x+3 =0#
#Delta = (-8)^2 -4(1)(3) = 52#

Since #Delta > 0#
this equation has 2 Real solutions.

(By the way, since #sqrt(Delta)# is irrational, both solutions are also irrational.)