How to use the discriminant to find out what type of solutions the equation has for #x^2 + 2x + 5 = 0#?

1 Answer
Don't Memorise
Jun 7, 2015

#x^2 + 2x + 5 = 0#

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

# = (2)^2-(4*1*5)#

# = 4-20=-16#

  • For #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 = -16#, this equation has NO REAL SOLUTIONS
- Note :
The solutions are normally found using the formula
#x=(-b+-sqrtDelta)/(2*a)#

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

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