How do you find the discriminant and how many solutions does #9u^2-24u+16# have?

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Answer 1 · 2015-05-13T06:49:24

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

#a=9, b=-24, c=16#

The Discriminant is given by:

#Delta=b^2-4*a*c#

# = (-24)^2-(4*(9)*16)#

# = 576-576=0#

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 = 0#, this equation has ONE REAL SOLUTION

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

As #Delta = 0#, #u = (-(-24)+-sqrt(0))/(2*9) = 24/18 = 4/3#