How do you find the discriminant and how many solutions does #x^2 -11x + 28 = 0# have?

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Answer 1 · 2015-05-05T07:42:44

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

#a=1, b=-11, c=28#

The Disciminant is given by :
#Delta=b^2-4*a*c#
# = (-11)^2-(4*1*28)#
# = 121-112=9#

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 = 9#, this equation has TWO REAL SOLUTIONS

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

As #Delta = 9#, #x = (-(-11)+-sqrt9)/(2*1) = (11+-3)/(2*1) = 14/2 or 8/2 = 7 or 4#

#x = 4,7# are the two solutions