Question

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

Answer 1

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

Let one zero be p

other zero is 7p

sum of zeroes = 8/3

p + 7p = 8/3

8p = 8/3

p= 1/3

Product of zeroes = 2k +1)/ 3

p( 7 p) = 2 k +1)/ 3

1/3 ( 7/3) = 2 k +1)/ 3

7/3 = 2 k + 1

2 k= 7/3 - 1

2k = 4/3

k= 2/3

Answer 2

p(x) = 3x² - 8x + 2k + 1

Let the one zero of p(x) be alpha (a).

Therefore, the other zero is 7 alpha (7a).

Now,

Sum of zeroes = - b/a

a + 7a = - (-8)/3

8a = 8/3

a = 1/3

Also,

Products of the zeroes = c/a

a × 7a = 2k+1/3

7a² = 2k+1/3

7(1/3) = 2k+1/3

7 = 2k+1

2k = 7-1

k = 6/2

k =3