What is the value of b+c if x^2+bx+c>0 only when x\in (-\infty, 2)\cup(2,\infty)?
+118626 What is the value of b+c if x^2+bx+c>0 only when \( x\in (-\infty, 2)\cup(2,\infty)?\)?
\(x^2+bx+c>0 \)
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
\(x^2+bx+c=(x-2)^2\\ b=-4,\;c=4\\ b+c=0 \)
