How to use the rational root theorem to list all possible rational roots?

Emmett Bradley

Emmett Bradley

Answered question

2023-02-25

How to use the rational root theorem to list all possible rational roots?

Answer & Explanation

ri2n1tv9pt

ri2n1tv9pt

Beginner2023-02-26Added 8 answers

f ( x ) = a 0 x n + a 1 x n - 1 + ... + a n - 1 x + a n
Any rational roots of f(x) = 0 may be expressed in lowest terms as p q , where p, p , q , q 0 , p is a divisor of a n , and q is a divisor of a 0 . To discover all the distinct fractions p q that arise, list all the possible integer factors of a 0 and a n , then all the potential rational roots. Consider the case when f ( x ) = 6 x 3 - 12 x 2 + 5 x + 10
a n = 10 has factors +-1, +-2, +-5 and +-10. (possible values of p); a 0 = 6 has factors +-1, +-2, +-3 and +-6. (possible values of q)
Possible fractions:
+-1/6, +-1/3, +-1/2, +-2/3, +-5/6, +-1, +-5/3, +-2, +-5/2, +-10/3, +-5, +-10

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