Question

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

Answer 1

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`).