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dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Algebra Problem

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?

Help?

zetafunc

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Registered: 2014-05-21

Posts: 2,436

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Re: Algebra Problem

When does

have integer roots?

Monox D. I-Fly

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From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Algebra Problem

When does

have integer roots?

When

is an integer, perhaps?

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thickhead

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Registered: 2016-04-16

Posts: 1,086

Re: Algebra Problem

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thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Algebra Problem

When does

have integer roots?

When

is an integer, perhaps?

In addition a and b have to be integers.
For a moment I thought "When

is an integer", is not enough since it is divided by 2 while finding roots. However I found it is o.k.
If a is odd a^2 is odd and a^2-4b is odd. and "-a +/- sqrt(a^2-4b)" will be even and the roots will be integers.
No problem also when a is even .

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}