In the x-y plane, did y=ax2+bx+c intersect with x-axis?

There are 3 variables (a,b and c) in a Quadratic function. In order to match the number of variables to the number of equations, we need 3 more equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that E is the correct answer choice. Using the condition 1) and the condition 2) at the same time, we get b2-4a(-3)=b2+12a and a>0. Hence, we get b2+12a>0. The answer is always yes and the equation intersects with the x-axis. Thus, the correct answer is C.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the original condition, there are 3 variables (a,k and p). In order to match the number of equations to the number of variables, we need 3 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that E is the correct answer. Using the condition 1) and the condition 2) at the same time, we get a diagram like the one attached.
If we look at the diagram, the graph passes through (k,p). As p>0, the graph intersects with x-axis. The answer is yes and the condition is sufficient. Hence, the correct answer is C.