The discriminant, which is b2-4ac, must be zero in 
order for this equation to have just one real root:



So we set this discriminant equal to zero:



Solve that either of two ways:

First way:



Add 16 to both sides:



Use the principle of square roots:

   <-- the answers 

Second way:



Factor the left side as the difference of two squares:



k-4 = 0;  k+4 = 0
  k = 4;    k = -4   <-- the answers

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To prove that  just has one
real root when k = 4 or k = -4, we substitute in



Substituting 4 for k:



Divide both sides by 2



Factor:



x-1 = 0; x-1 = 0
  x = 1   x = 1   <-- just 1 root, 1

---



Substituting -4 for k:





Divide both sides by 2



Factor:



x+1 = 0;  x+1 = 0
  x = -1    x = -1   <-- just 1 root, -1

Edwin