Question 618980
<font face="Times New Roman" size="+2">


Re-write your equation in standard form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x^2\ -\ 8x\ -\ (2k\ +\ 1)\ =\ 0]


Use the quadratic formula where *[tex \LARGE a\ =\ 3], *[tex \LARGE b\ =\ -8], and *[tex \LARGE c\ =\ -(2k\ +\ 1)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{-(-8)\ \pm\ \sqrt{(-8)^2\ -\ 4(3)(-(2k\ +\ 1))}}{2(3)}]


Which simplifies to


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{8\ \pm\ \sqrt{76\ +\ 24k}}{6}]


Since one root is 7 times the other:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{8\ +\ \sqrt{76\ +\ 24k}}{6}\ =\ 7\left(\frac{8\ -\ \sqrt{76\ +\ 24k}}{6}\right)]


Solve for *[tex \LARGE k], then use that value to calculate the value of the two roots.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>