Question

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

Answer 1

let one root be p
then second root will be seven time = 7p
sum of root = -b/a
p+ 7p = -(-8)/3
8p = 8/3
p =1/3
product of root = c/a
7p × p = (2k +1)/3
7(1/3)^2 = (2k +1)/3
7/9=(2k+1)/3
7= 3(2k+1)
7= 6k +3
4=6k
k = 2/3

Answer 2

Hey

Here is your answer,

Let the roots be a and 7a.

3x^2-8x+2k+1 = 0

Sum of zeroes = -b/a
a + 7a = 8/3
8a = 8/3
a = 1/3

Product of zeroes = c/a
a x 7a = 2k + 1 /3
7a^2 = 2k+1/3
7 x (1/3)^2 = 2k + 1 /3
7/9 = 2k+1/3
7/3 = 2k +1
7 = 6k +3
6k = 7-3
k = 4/6
k = 2/3

Hope it helps you!