Two numbers $$b$$ and $$c$$ are chosen at random (with the replacement from the numbers $$1,2,3 \ldots 9$$ ) . The probability that $$x^{2} + bx + c > 0$$ for all $$x \in R$$.
$$\text{Details and Assumptions :-}$$ Let the probability could be represented as $$\dfrac{A}{B}$$ ,then find $$A+B$$ .