Rational Root Theorem By: Yu, Juan, Emily. What Is It? It is a theorem used to provide a complete list of all of the possible rational roots of the polynomial.

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Presentation transcript:

Rational Root Theorem By: Yu, Juan, Emily

What Is It? It is a theorem used to provide a complete list of all of the possible rational roots of the polynomial.

How To Use It? First locate your q and p value. Example: 6x 4 - 2x 3 + 5x 2 + x -10 = 0 Your q would be 6 and your p value would be -10 because of 6 is your leading coefficient and -10 is your constant. (q = leading coefficient; first number of your polynomial, p = constant; last number of your coefficient) Next you list all the possible factors of both the coefficient and constant; your q and p. 6: ±(1, 2, 3, 6) -10: ±(1, 2, 5, 10 )

How To Use It? After listing out all of the factors of your leading coefficient and constant; your q and p. You would want to make a list of all of your possible zeros by dividing your p (leading coefficient) by your q (Constant). Using the example on the previous slide, your list of all of the possible zeros would be: p/q = ±(1, 2, 5, 10, ½, 5/2, 10/2, 1/3, 2/3, 5/3, 10/3, 1/6, 5/6, 10/6)

How To Use It? After that, with the list you came up with; p/q = ±(1, 2, 5, 10, ½, 5/2, 10/2, 1/3, 2/3, 5/3, 10/3, 1/6, 5/6, 10/6), those would be your possible zeros. Refer to the link below if you have further questions.

How To Use It? Once you have your list of all of your possible zeros, using synthetic division; you can find your exact zeros for your polynomial. Refer to the link below for a review of Synthetic division:

Practice Problem 4x 3 + 8x Use the Rational Root Theorem for the polynomial above. Once you find the possible zeros for the polynomial equation above, use Synthetic division to find the exact zeros.