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Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 22, 2011"

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Solution: If there is only one integer root, if it is in the form <math>x - y</math>, and <math>y</math> is a constant, then <math>y</math> must be a factor of <math>25</math>, the polynomial's constant term, because of the Factor Theorem. <math>-1</math> and <math>1</math> are not zeros. Going up from there, we see that <math>5</math> is a zero, so our answer is <math>5</math>.
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==Problem==
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{{:AoPSWiki:Problem of the Day/July 22, 2011}}
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==Solution==
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If there is only one integer root, if it is in the form <math>x - y</math>, and <math>y</math> is a constant, then <math>y</math> must be a factor of <math>25</math>, the polynomial's constant term, because of the Factor Theorem. <math>-1</math> and <math>1</math> are not zeros. Going up from there, we see that <math>5</math> is a zero, so our answer is <math>5</math>.
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[[Category: Intermediate Algebra Problems]]

Latest revision as of 14:41, 22 July 2011

Problem

AoPSWiki:Problem of the Day/July 22, 2011

Solution

If there is only one integer root, if it is in the form $x - y$, and $y$ is a constant, then $y$ must be a factor of $25$, the polynomial's constant term, because of the Factor Theorem. $-1$ and $1$ are not zeros. Going up from there, we see that $5$ is a zero, so our answer is $5$.

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