How do you find the discriminant and how many solutions does #x^2 + 8x + 16 = 0# have?

1 Answer
Apr 29, 2015

Equations of the form #Ax^2+Bx+C=0#

Discriminant=#D=sqrt(B^2-4AC)=8^2-4*1*16=0#
which means there is one solution
For #D>0# there would be two solutions,
for #D<0# there would be no (real) solution.

Without working out the discriminant, it's fairly easy to see that:
#->(x+4)^2=0->x=-4#
In the graph you see the standard #x^2#-graph moved by #-4#
graph{x^2+8x+16 [-15.5, 4.5, -2.4, 7.6]}