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

Answer 1

Eva Adamson

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

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.