If the quadratic formula of a quadratic function yields 14, how many unique real and complex zero(s) does the function have?

1 Answer
Alan P.
Oct 28, 2015

If the quadratic formula for a quadratic yields a single Real value, the the quadratic has one real zero (and no complex zeros).

Explanation:

Within the quadratic formula, the discriminant, #Delta = b^2-4ac# determines the number and type of roots (zeroes) based on the following rule:

#{: ( > 0, rArr, "two Real roots"), ( = 0, rArr ,"one Real root"), (< 0,rArr,"two Complex roots") :}#

An examination of the quadratic formula:
#color(white)("XXX")x= (-b+-sqrt(Delta))/(2a)#
should make the reasons clear.

If #Delta != 0# then the quadratic formula gives two solutions:
one with a component #+sqrt(Delta)# and
one with a component #-sqrt(Delta)#

If there is a single solution then #+-sqrt(Delta)# must equal #+-0# (i.e. #Delta = 0#).

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