Question 234430
<font face="Garamond" size="+2">


Calculate the discriminant:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \Delta\ =\ b^2\ - 4ac], where *[tex \LARGE a], *[tex \LARGE b], and *[tex \LARGE c] are the lead, 1st degree, and constant coefficients of the quadratic equation in standard form.  Then:


*[tex \LARGE \Delta > 0 \ \ \Rightarrow\ \] Two real and unequal roots.  If the discriminant is a perfect square, then the roots are rational, otherwise they ar e irrational.


*[tex \LARGE \Delta = 0 \ \ \Rightarrow\ \] One real root with a multiplicity of two.  That is to say that the trinomial is a perfect square and has two identical factors.


*[tex \LARGE \Delta < 0 \ \ \Rightarrow\ \] A conjugate pair of complex roots of the form *[tex \LARGE a \pm bi] where *[tex \LARGE i] is the imaginary number defined by *[tex \LARGE i^2 = -1]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>