find the value of k if the quadratic polynomial x2+8x+k has zeroes whoose difference is 2 ?

Let the zeros of quadratic polynomial be a and b

So, a+b = -8 (Sum of roots of  a quadratic equation is equal to -8 (-b/a))

Also, its given that a-b = 2 

Hence solving the above 2 equations 

2a = -6

a = -3 and b = -5

 

Now k = product of roots

Hence, k = -5*-3

k = 15