Question

if the product of of he zeroes of the quadractic polynomil
p(x)=(k-2)x²- 4x + k is 3 write the value of k

Answer 1

when the zeroes of the polynomial is α and β, the equation becomes
x²-(α+β)x +αβ =0
comparing this with the given equation,
k/(k-2) = 3
⇒k =3k -6
⇒2k =6
⇒k =3

Answer 2

We are given that the product of the zeros of the given quadratic  equation is 3

αβ = c/a

      = k/k-2 = 3 (given)

       = k = 3(k-2)
       = k  = 3k - 6
        = k - 3k = -6
       =  2k   = 6
        = k  = 3