How do you find the discriminant and how many solutions does #-7d^2 + 2d + 9 = 0# have?

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Answer 1 · 2015-05-11T11:51:42

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

#a=-7, b=2, c=9#

The Disciminant is given by :
#Delta=b^2-4*a*c#
# = (2)^2-(4*(-7)*9)#
# = 4-(-252)=4+252=256#

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 = 256#, this equation has TWO REAL SOLUTIONS

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

As #Delta = 256#, #x = (-(2)+-sqrt256)/(2*-7) = (-2+-16)/(-14) = 14/-14 or (-18)/-14 = -1 or 9/7#

#color(green)(x = -1,9/7# are the two solutions