How do you find the discriminant and how many and what type of solutions does #4x^2-2x+1=0# have?

1 Answer
May 5, 2015

The equation is of the form #color(blue)(ax^2+bx+c=0# where:

#a=4, b=-2, c=1#

The Disciminant is given by :
#Delta=b^2-4*a*c#
# = (-2)^2-(4*4*1)#
# = 4-16=-12#

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

As #Delta = -12#, this equation has NO REAL SOLUTIONS

  • Note :
    The solutions are normally found using the formula
    #x=(-b+-sqrtDelta)/(2*a)#

Substituting the value of #Delta# will give us 2 imaginary roots/solutions.