Question 551052
f(x) = x^2 -11x + k
g(x) = x^2 -14x + 2k
.
x = 0 defines the roots
But that reveals we would be looking for a point where k = 2k.
That exists only at k=0.
Given k=0, we can redefine f(x) and g(x):
f(x) = x*(x-11)
g(x) = x*(x-14)
They share the common root 0.
.
{{{ graph(500,500,-5,20,-40,5,x^2-11*x+0,x^2-14*x+2*0) }}}