Question

PRE CALC PLEASE HELP!!!

Topic: Rational Functions

If f(x)=2x^3-bx^2+cx+12, Were b and c integers, list all possible rational roots of f(x)

Answer 1

Answer:
`\bold{\pm \{1, 2, 3, 4, 6, 12, (1)/(2), (3)/(2)\}}`

Explanation:

Q P

f(x) = 2x³ - bx² + cx + 12

Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative signs.

`\quad \pm \frac{\text{factors of P}}{\text{factors of Q}}\\\\=\pm \frac{\text{factors of 12}}{\text{factors of 2}}\\\\=\pm (1,2,3,4,6,12)/(1,2)\\\\=\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm (1)/(2), \pm (3)/(2)\\`