Question

Which correctly describes the roots of the following 
cubic equation?
x  – 5x  + 3x + 9 = 0

Answer 1

Emily, please make the equation you provided into a cubic equation by typing in the appropriate powers of x. For example, the cube of x is written as x^3.

Answer 2

Of course, we could actually find the roots of the (cubic) equation. The number of + roots and the number of - roots would be pretty obvious, then.

Answer 3

A more sophisticated approach would be to count the number of sign changes in your (cubic) function. (I count 2.) Surely some other OpenStudy participant can clarify for us how that count of sign changes can be used to predict how many + and how many - roots there'll be. (I've forgotten.)

Answer 4

i meant to put x^3

Answer 5

Please do; it'll be worth the effort.

Answer 6

While waiting for your response, I've done an Internet search and have found a citation of "Descartes' Rule of Signs." If you're interested, look that up (or do an Internet search).

Answer 7

okay thanks i appreciate it