What is the value of b+c if x^2+bx+c>0 only when x∈(−∞,2)∪(2,∞)??
x2+bx+c>0
this is a concave up parabola.
If this function is greater than zero for all values of x except for x=2 then the vertex is (2,0)
And there will only be one root.
so
x2+bx+c=(x−2)2b=−4,c=4b+c=0