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 constant coefficient by $1$. After some time, $x^2 + 20x + 10$ 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?

Guest Jun 14, 2017

#1**+1 **

I remember this question from a while back....

Maybe this will help some: https://web2.0calc.com/questions/need-help_79514

Elaborating on this...

x^{2} + bx + c When b is one greater than c , we can say...

x^{2} + (c+1)x + c Which can be factored as...

(x + 1)(x + c) And so the roots will be x = -1 and x = -c , which will always be an initeger

hectictar
Jun 14, 2017