Question

According to the rational root theorem, which of the following are possible roots of the polynomial function F(x) = 4x^3 - 6x^2 + 9x + 10?

A) 2
B) 5
C) 1
D) -2
E) 5
F) 6

Answer 1

The possible roots of the polynomial function 4x^3 - 6x^2 + 9x + 10 are 1/4, 1/2, 5/4, and 5/2.

Step-by-step explanation:

The rational root theorem states that if a polynomial function has a rational root, then that root must be a factor of the constant term divided by a factor of the leading coefficient. In this case, the constant term is 10 and the leading coefficient is 4. Therefore, we can test the possible roots by finding factors of 10 and dividing them by factors of 4.

Factors of 10 are 1, 2, 5, and 10. Factors of 4 are 1 and 2. Dividing the factors of 10 by the factors of 4, we get 1/4, 2/4 (which simplifies to 1/2), 5/4, and 10/4 (which simplifies to 5/2).

Therefore, the possible roots of the polynomial function F(x) = 4x^3 - 6x^2 + 9x + 10 are 1/4, 1/2, 5/4, and 5/2.