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A root of $x^{2}+b x+c=0$ is an integer and $b$ and $c$ are integers. Explain why the root must be a factor of $c .$

Therefore the root is a factor of c.

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 7

Sum and Product of the Roots of a Quadratic Equation

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Lectures

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If B and C are imagers, why do the routes have to be factors of C? Well, it's this fact right here in first of all, they can you see how they didn't give you in a value that means a is one. And so this really could be rewritten as route one times route to equals C over one. Well, that see? And so, of course, they have to be factors if this is an imager than there, two factors that have to get you there. And so, of course, it has to be a factor because these you multiply the routes to get to this ultimate product here. One final thing before I wrap this up is they actually give us one more piece of information. One of these routes is an imager. And so say it was five, and this is 20 25. Now let's make it 35 times blank equals 30. It doesn't really matter, but like, if it's, ah whole number time something to be another hole number, there's no way this could be a decimal, a fraction. So if one is a whole number time, something to get a product of a whole number, for sure, the other route also has to be a whole number or an imager.

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