Factor and cubes

Question

Find all possible zeroes of 4x^5 + 3x^2 + 2x + 6

a. Plus/minus .25

b. Plus/minus 2/3

c. Plus/minus 3

d. .5

e. All of the above

Answer 1

P = {+-1, +-2, +-3, +-6}

Q = {+-1,+-2,+-4}

P/Q = {+-1, +-1/2, +-1/4, +-2, +-3, +-3/2, +-3/4, +-6}

NONE of them work... so there are no rational solutions

therefore the solutions must be found numerically, perhaps by

Newton's method, bisection method, or most easily by carefully

examining the graph.

the approximate solution is -1.137

the other four (4) solutions are complex/imaginary