Question 462365
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The easiest way to do these, rather than doing a bunch of trial and error, is to set the trinomial equal to zero and solve the quadratic equation using the quadratic formula.


In this case the discriminant:  *[tex \LARGE \Delta\ =\ b^2\ -\ 4ac\ = 169\ -\ 144\ =\ 25]


is a perfect square so we know that the trinomial factors over the rationals.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{-b\ \pm\ \sqrt{b^2\ -\ 4ac}}{2a}\ =\ \frac{13\ \pm\ 5}{12}]


So *[tex \Large x\ =\ \frac{3}{2},\ \ ] or *[tex \Large x\ =\ \frac{2}{3}]


Therefore the factors are:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2x\ -\ 3)(3x\ -\ 2)]



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