The equations $x^2−4x+k=0$ and $x^2+kx−4=0$, where $k$ is a real number, have exactly one common root. What is the value of $k$?
I know the answer but can it be done with the relation of roots. $a$ and $b$ are roots of equation 1 and $a$ and $c$ are roots of equation 2. So the relations are :-
- $a + b = 4$
- $ab = k$
- $a + c = (-k)$
- $ac= (-4)$
I tried doing all the stuff but couldn't get it. Can we find it using these 4 equations?