The quadratic equation x^2 + 4kx+2(k+1) = 0 has equal roots, find the possible values of k.

For a quadratic equation ax^2 +bx +c = 0 with equal roots we know the discriminant b^2-4ac must equal 0. From our equation we have a=1, b=4k and c=2(k+1) so using b^2-4ac = 0 we have (4k)^2 -412(k+1) = 0 Expanding we get 16k^2-8k-8 = 0 Now we have a quadratic in k to solve, to make it easier we can start by dividing by 8 to give us 2k^2-k-1 = 0 Which factorises to (2k+1)(k-1) = 0 So we have 2k+1=0 and k-1=0 which gives us k=-1/2 and k=1 respectively. So these are our values of k that give the quadratic equation x^2+4kx+2(k+1) = 0 equal roots.