168k views
1 vote
F(x) = 4x^3+...+ 9
list all possible rational zeroes of the function​

1 Answer

3 votes

The Rational Root Theorem says any rational zeros of f must be a fraction with a factor of the constant (9 here) in the numerator and a factor of the leading coefficient (4 here) in the denominator. We have to include negative factors.

Factors of 9: -9, -3, -1, 1, 3, 9

Factors of 4: 1, 2, 4

We only have to consider negative numbers for the numerator to get all the possible values.

We just make the list, going through all the numerators one denominator at a time.

Possible rational zeros, i.e. possible rational values for x such that f(x)=0 are

Answer: -9, -3, -1, 1, 3, 9, -9/2, -3/2, -1/2, 1/2, 3/2, 9/2, -9/4, -3/4, -1/4, 1/4, 3/4, 9/4

User Johannes Jander
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories