Question 271022
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For a quadratic equation in standard form, namely:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ ax^2\ +\ bx\ +\ c\ =\ 0]


the discriminant, *[tex \Large \Delta], is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \Delta\ =\ b^2\ -\ 4ac]


*[tex \LARGE \Delta > 0 \ \ \Rightarrow\ \] Two real and unequal roots.  If the discriminant is a perfect square, the roots are rational.  Otherwise not.


*[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]
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