Answers

2015-10-01T11:35:33+05:30
The polynomial equation is in the form of  x^{2} -(a+7a)x + (a)(7a)
Where a and 7a are the two roots.
So let the given equation be:
 x^{2} - \frac{8}{3}x+[tex] \frac{2k}{3} + \frac{1}{3} [/tex]

Comparing both:
Sum of zeroes:
a+7a=  \frac{8}{3}
8a =   \frac{8}{3}
a = 1/3

Product of zeroes:
(a)(7a)= \frac{2k}{3} + \frac{1}{3} [/tex]
( \frac{1}{3} )( \frac{7}{3} ) =  \frac{2k+1}{3}
 \frac{7}{3} = 2k+1
7 = 3(2k+1)
7 = 6k+3
6k = 4
k =  \frac{4}{6} = \frac{2}{3}
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