Question

What are the possible rational zeros of f(x) = x4 - 4x3 + 9x2 + 5x + 14

Answer 1

the ration zero theorem says find the factors of the constant and let them be q

find the factors of the coefficient of the leading term and let them be p

then the possible rational zeros will be q/p

so you are looking at

\[\pm 1,\pm 2, \pm 7, \pm 14\]

Answer 2

thank you @campbell_st can you answer this question as well?
What are the possible number of positive real, negative real, and complex zeros of f(x) = 4x3 + x2 + 10x - 14

Answer 3

i got 1,3,9

Answer 4

plus or minus

Answer 5

well the factors of the constant are \[q = \pm 1, \pm 2, \pm 7, \pm 14\]

and the leading term is \[p = \pm1, \pm2, \pm4\]

so you need to now write them as

\[\frac{q}{p} = \frac{\pm1}{\pm1}, \frac{\pm2}{\pm1}, \frac{\pm7}{\pm1} \frac{\pm14}{\pm1}\]

and do the same with a denominator or 2 and repeat agaib with a denominator of 4

hope it helps

Answer 6

thank you