How do you use the discriminant to determine the nature of the roots for #x^2 + 2x + 5 = 0#?

1 Answer
Don't Memorise
Jun 19, 2015

As #color(red)(Delta = -16#(less than zero), this equation has two complex roots.

Explanation:

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

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=2, c=5#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (2)^2-(4*(1)*5)#
# = 4-20=-16#

When, #Delta<0# there are two complex solutions.
Here, #color(red)(Delta = -16)#, so this equation has two complex roots

  • Note :
    The solutions are normally found using the formula
    #x=(-b+-sqrtDelta)/(2*a)#
    Finding the solutions:
    # x =( -2+-sqrt-16)/(2a#
    #color(red)( x =( -2+4i)/2# and #color(red)(x = (-2-4i)/2#
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