Question 247384
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Compute the discriminant. The discriminant is the part of the quadratic formula *[tex \LARGE \left( x = \frac{-b\ \pm\ \sqrt{b^2\ -\ 4ac}}{2a}\right) ], that is under the radical, namely *[tex \LARGE \Delta\ =\ b^2\ -\ 4ac]


*[tex \LARGE \Delta > 0 \ \ \Rightarrow\ \] Two real and unequal roots.  If *[tex \LARGE \Delta] is a perfect square, then the roots are rational numbers, otherwise the roots are 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\ \] No real solutions. Rather you have 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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