Question

Which of the following represents the set of possible rational roots for the polynomial shown below?

x^3+5x^2-8x-20=0

A.{1/2, 1,2, 5/2, 4, 5, 10, 20}
B. {+/-1, +/-2, +/-4, +/-5, +/-10}
C. {+/-1/2, +/-1, +/-2, +/-5/2, +/-4, +/-5, +/-10, +/-20}
D. {+/-2/5, +/-1/2, +/-1, +/-2, +/-2/5, +/-1/5, +/-1/10}

Answer 1

You want to write out the factors of 20 (the last number) first:
1, 2, 4, 5, 10, 20
Lets call these guys 'p'

Then you want to write out the factors of the leading coefficient (the number in front of the highest power of x):
1
Lets call this guy 'q'

Then you want to create all the possible fractions you can with:
\[\pm \frac{p}{q}\]
Since q is just 1, we are lucky, so the possible rational roots are:
\[\pm \frac{1}{1}, \pm \frac{2}{1}, \pm \frac{4}{1}, \pm \frac{5}{1}. \pm \frac{10}{1}, \pm \frac{20}{1}\]

Answer 2

This is called the Rational Roots Theorem.
http://www.mathwords.com/r/rational_root_theorem.htm

Answer 3

If you need anything explained in more detail just ask :)

Answer 4

thank you :)