Question 391016
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Begin with:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \rho(x)\ =\ ax^2\ +\ bx\ +\ c]


Since the roots are 0 and 1 we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \rho(0)\ =\ a(0)^2\ +\ b(0)\ +\ c\ =\ 0]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \rho(1)\ =\ a(1)^2\ +\ b(1)\ +\ c\ =\ 0]


Since *[tex \Large \left(\frac{1}{2},-\frac{2}{33}\right)] is a point on the graph, we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \rho\left(\frac{1}{2}\right)\ =\ a\left(\frac{1}{2}\right)^2\ +\ b\left(\frac{1}{2}\right)\ +\ c\ =\ -\frac{2}{33}]


Giving us the 3X3 system:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{4}a\ +\ \frac{1}{2}b\ +\ c\ =\ -\frac{2}{33}]


Solve the system to get your coefficients.


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