Question

What are the possible rational zeros of f(x) = 2x3 – 4x2 – 7x + 10 ?

± 1/2, ± 1, ± 2, ±5/2 , ± 5, ± 10

± 1, ± 2, ± 5, ± 10

1/2 , 1, 2, 5/2 , 5, 10

1, 2, 5, 10

Answer 1

this applies to the rational root thrm that takes a pool of options from the factors of the last number divided by the factors of the first

Answer 2

the factors of the constant are called p

factors of the coefficient of the leading term are q

the possible roots are p/q

Answer 3

i still dont understand

Answer 4

you need to be able to determine the first and last numbers to begin with :) can you tell me what they are?

Answer 5

also, proper form has the +- tags, so that narrows it down to the first 2 options

Answer 6

ok... so the factors of 10 are 1 x 10 or -1 x -10, 2 x 5 or -2 x -5 (called p)

the factors of 2 are 1 x 2 or -1 x -2 (called q)

so if you use p/q for the roots you will have

1/1, -1/1 1/-1 and -1/-1, then 10/1, -10/1, 10/-1 and -10/-1, 1/2, -1/2, 1/-2, -1/-2 etc...

this gives all the possible rational roots