Question

if one zero of a polynomial 3x2-8x+2k+1 is seven times the other ,find the value of k

Answer 1

let one zero is "a" so the other zero becomes "7a"
now according to question
a and 7a are zeroes of polynomial
so
(a + 7a) = -(-8)/3
$sum \: of \: zeroes \: = \frac{ - b}{a}$
8a = 8/3
a = 1/3
also
(a)(7a) = (2k+1)/3
$product \: of \: zeroes = \frac{c}{a}$
7(a^2)=(2k+1)/3
7× [(1/3)^2] = (2k+1)/3
(7/9)×3 = 2k + 1
7 = 6k + 3
6k = 4
k = 2/3

Answer 2

Required answer is in the attachment.