Find the value of K

since -4 is a root of the given quad.eqn,

So,

x=-4 must satisfy that equation.

i.e. on putting x=-4, the LHS must be equal to the RHS.

so, we get,

16-4P-4=0

i.e.

p=3

So the other equation becomes,

(x*x)+4x+k=0

this  equation has equal roots.So, the value of the discriminant for that eqn must be equal to zero.

So,

16-4k=0

which gives us that

k=4