In a math class, the quadratic $x^2 + 10x + 20$ is written on the board. Each student goes to the board and increases or decreases either the linear or

In a math class, the quadratic  is written on the board. Each student goes to the board and increases or decreases either the linear or constant coefficient by . After some time,  is written on the board. Did a quadratic with integer roots necessarily appear on the board at some time during this process? Why or why not?

Explain, in words, all of the steps in your solution. Use complete sentences. Write as though the person reading is one of your classmates who has not seen the problem before. Include any important observations you made and explain why you are doing anything that isn't totally obvious.