How do you solve #x^2 - 2x - 3 = 0# using the quadratic formula?

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Answer 1 · 2015-06-12T08:31:23

the solutions are
# color(green)(x= 3 #
# color(green)( x=-1#

#x^2 - 2x - 3 = 0#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-2, c=-3#

The Discriminant is given by:
#Delta=b^2-(4*a*c)#

# = (-2)^2-(4*1*(-3))#
# = 4 + 12= 16#

As #Delta>0# there are two solutions,

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

As #Delta = 16#, #x = (-(-2)+-sqrt(16))/(2*1) = (2+-4)/2#

the solutions are
# color(green)(x= 6/2 = 3 #
# color(green)( x=-2/2=-1#