Question 767352
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No answer.


If *[tex \LARGE ax^2\ +\ bx\ +\ c\ =\ 0] has a root of -2 with a multiplicity of 2, then the polynomial must factor to *[tex \LARGE \left(\alpha x\ +\ \beta\right)^2] where *[tex \LARGE \alpha^2\ =\ a] and *[tex \LARGE \beta^2\ =\ c]


So if *[tex \LARGE \alpha x\ +\ \beta\ =\ 0] and the root is *[tex \LARGE -2] and *[tex \LARGE \alpha^2\ =\ 4], then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2(-2)\ +\ \beta\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \beta =\ 4]


So *[tex \LARGE 4x^2\ +\ kx\ +\ 6\ =\ 0]


must factor to *[tex \LARGE (2x\ +\ 4)^2\ =\ 0].  The problem is, when you multiply it out, you get *[tex \LARGE 4x^2\ +\ 16x\ +\ 16\ =\ 0].


Doesn't work.  Either there is no solution, or you wrote the problem incorrectly.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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