Question

If one zero of the polynomial 3x2 - 8x 2k 1 is seven times of other then find the value of k

Answer 1

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 = $\frac{4}{6} = \frac{2}{3}$

Answer 2

hope this is helpful