How do you find the discriminant and how many solutions does #9x^2-6x+1=0# have?

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Answer 1 · 2015-04-30T12:20:19

The equation is of the form #Ax^2+Bx+C=0# where:

#A=9, B=-6, C=1#

Now the disciminant
#D=B^2-4*A*C=#
#(-6)^2-4*9*1=#
#36-36=0#

If #D=0# then there is only one solution.
(for #D>0# there are two solutions,
for #D<0# there are no real solutions)

Extra:
The solutions are normally found by working out:

#x=(-B+sqrtD)/(2*A) or x=(-B-sqrtD)/(2*A)#

But since #D=0# in this case it comes down to:

#x=(-B)/(2*A)=(-(-6))/(2*9)=1/3#

This means the graph (a 'valley'-parabola) will just touch the #x#-axis at the point #(1/3,0)#