Question

Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x4 + 3x3 - 5x2 - 9x - 2

I'm not sure of what is meant by, "Find all the zeros of the function." ...or a rational zero...

May someone please explain step by step how to solve this

Answer 1

\[f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2\]

Answer 2

use the rational roots thrm to determine a pool of rational root options

Answer 3

a rational root is just a rational number (a fraction or integer) that makes the setup equal to zero

Answer 4

I'm not very knowledgeable on this...but is the rational root theorem suosed to be applied?
\[\pm 1, \pm3, \] from \[3x^2\] and \[\pm 1, \pm3, \pm9\] from \[9x\]

Answer 5

no, the rational roots thrm says that the factors of the constant, divided by the factors of the highest degree coefficient, create a pool of viable options for roots.

Answer 6

in this case, 2 is the constant, and 1 is the coefficient of highest degree giving us th e options:\[\pm\frac{1,2}{1}\]

Answer 7

as such, either 1,-1, 2,-2 can form roots to this equation

we can also use the decartes sign rule to manage the positive and negative roots if need be

Answer 8

the decartes sign rule?