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

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, $\Delta = {b}^{2} - 4 a c$ 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:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- b \pm \sqrt{\Delta}}{2 a}$
should make the reasons clear.

If $\Delta \ne 0$ 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 $\pm \sqrt{\Delta}$ must equal $\pm 0$ (i.e. $\Delta = 0$).