Question

if one zero of the polynomial 3 x2 - 8 x + 2 k + 1 is 7 times the other find the value of k

Answer 1

p(x) = 3x² -8x + 2k + 1

now A/Q  one root is 7 times other........let 2 roots be a and b
⇒  a=7b

now we know  sum of roots = a+b = 7b + b = 8b = -(-8/1) = 8
⇒ b = 1    and  a= 7

now product of roots = ab = 2k+1 ⇒ 7 = 2k + 1
⇒ 2k = 6 ⇒ k =3

hope this helps.

Answer 2

Hi there !!

p(x) = 3x² -8x + 2k + 1

Let α and β be the zeros
 α =7β

  sum of zeros =  α + β
                       = 7β + β
                       = 8β =  8               [ -b/a ] 

 β = 1

α = 7

product of zeros = αβ  = 7 x 1 = 7

c/a =  2k+1  = 7

                        
2k + 1 = 7

2k = 7 - 1

2k = 6

k = 3