How do you find the discriminant and how many and what type of solutions does #x^2 - 5x = 6# have?

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Answer 1 · 2015-05-10T18:09:59

discriminant # D= b^2 - 4ac #

the equation can be written as:
# x^2 - 5x -6 = 0#

here:
#a =1#
#b =-5#
#c = -6#
(the coefficients of #x^2# , #x# and the constant term respectively)

# D= b^2 - 4ac = (-5^2) - (4 xx 1 xx -6)#
# D= 25 + 24 = 49#

formula for roots :

# x = (-b +- sqrt D) / (2a) = (5 +- sqrt 49) / 2#

# x = (5 +7) / 2 = 12 /2# and

#(5 -7) /2 = -2/2#

#x# has two solutions:
# x = 6# and # x = -1#
since # D >0# the solutions are real and unequal