Question 193802
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Rewrite your equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x^2 + 8x + 0 = 0]


So:


*[tex \LARGE  a = 4]


*[tex \LARGE  b = 8]


*[tex \LARGE  c = 0]


Discriminant:


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


Plug in the values and calculate.  


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \Delta = 0 \ \ \Rightarrow\ \] One point of intersection (the x-axis is tangent to the curve at the vertex)


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \Delta > 0 \ \ \Rightarrow\ \] Two points of intersection, i.e. two real number roots.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \Delta < 0 \ \ \Rightarrow\ \] No points of intersection, i.e. the roots are a conjugate pair of complex numbers.



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