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

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

 

Elaborating on this...

 

x2 + bx + c             When  b  is one greater than  c  , we can say...

x2 + (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
edited by hectictar  Jun 15, 2017

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