Assignment #2 - Due 1.30.12

# Assignment #2 - Due 1.30.12 - First multiply this equation...

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1. I found the following on a math-help website as a response to the question “How do you prove the Rational Roots Theorem?”: The theorem states that if a polynomial has a rational root, then the denominator of the root must divide the coefficient of the highest power term of the polynomial, and the numerator of the root must divide the constant term of the polynomial. Start with a general polynomial equation with integer coefficients. We can suppose that x is a rational root. Therefore it takes the form of x=r/s, where r and s are integers and s is not equal to zero. S0r/s is reduced to lowest terms (so r and s have no common factor).

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Unformatted text preview: First multiply this equation through by . You'll see that all but the first term are integers, and the first term is . That implies that must be an integer, so s divides evenly into Since r and s have no common factor, it must be that s divides evenly into . Next multiply the equation through by . You'll see that all but the last term are integers, and the last term is . You are finished! Expand on the above comments to write a different proof of the rational roots theorem. (“Different” in that it will be different than the one we did in class.)...
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