Open Middle®
Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to so that there is only one integer solution. Note that you can use a 05 to make a 5.
Hint
How could you find the equation if you already knew the solutions?
Answer
The possible answers are: 4x^2 + 12x + 09, 4x^2 + 36x + 81, 9x^2 + 12x + 04, 9x^2 + 24x + 16, 9x^2 + 30x + 25, 9x^2 + 54x + 81
Source: Daniel Luevanos
Should this say “so that there is only one solution” instead of “so that the solutions are integers”?
Thanks Michael. We’ve updated the problem. Let us know if there are any other issues.
3x^2+18x+27=0
3(x+3)^2=0
x=-3
I *think* that’s the only case where you can dilate a parabola where a=1 (initially) that doesn’t repeat numbers or get too large.