Rational Root Theorem

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Rational Root Theorem

• By Yu, Juan, Emily

2
What Is It?

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

3
How To Use It?

• First locate your q and p value.
• Example
• 6x4 - 2x3 5x2 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 )

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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)

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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.
• http//www.youtube.com/watch?vRXKfaQemt

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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
• http//www.youtube.com/watch?vbZoMz1Cy1T4

7
Practice Problem

• 4x3 8x2 16
• 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.