Question 462366
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2r^2\ +\ 5x\ +\ 4]


Calculate the discriminant:  *[tex \Large b^2\ -\ 4ac\ =\ 25\ -\ 32\ = -7]


Since the discriminant is not a perfect square, the trinomial does not factor over the rationals.


Set the trinomial equal to zero and use the quadratic formula to determine the two complex roots.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r\ =\ \frac{-b\ \pm\ \sqrt{b^2\ -\ 4ac}}{2a}\ =\ \frac{-5\ \pm\ i\sqrt{7}}{4}]


Then the factors are:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2r^2\ +\ 5x\ +\ 4\ =\ \left(r\ -\ \left(\frac{-5\ +\ i\sqrt{7}}{4}\right)\right)\left(r\ -\ \left(\frac{-5\ -\ i\sqrt{7}}{4}\right)\right)]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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