How do you find the discriminant and how many and what type of solutions does #7x^2+8x+1=0# have?

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Answer 1 · 2015-05-05T07:46:31

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

#a=7, b=8, c=1#

The Disciminant is given by :
#Delta=b^2-4*a*c#
# = (8)^2-(4*7*1)#
# = 64-28=36#

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 = 36#, this equation has TWO REAL SOLUTIONS

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

As #Delta = 36#, #x = (-(8)+-sqrt36)/(2*7) = (-8+-6)/(2*7) = -2/14 or -14/14 = -1/7 or -1#

#x = -1/7,-1# are the two solutions