If one of the zero of the quadratic polynomial . . .

Question : If one of the zero of the quadratic polynomial (k-1)x²+kx+1 is -3, then the value of k is 

a) -4/3

b) 4/3

c) 2/3

d) -2/3

Doubt by Zoha

Solution :

p(x) = (k-1)x²+kx+1 is -3

-3 is the zero of p(x)

p(-3) = 0

(k-1)(-3)²+k(-3)+1 = 0
(k-1)(9)-3k+1 = 0
9k-9-3k+1 = 0
6k-8 = 0
6k = 8
k = 8/6
k = 4/3

Hence, b) would be the correct option.