Question

algebra 2 help
Use the rational root theorem to determine all possible rational roots of 5x^3+4x^2+4x+10=0. do not find the actual roots.

For 2x^5-5x^3+12=0, state the number of complex roots, the possible number of real roots and the possible rational roots.

Answer 1

The Rational Root Theorem (RRT) states that if there are rational roots, they must be of the form:

p/q,

where p is a divider of the constant term,
and q is a divider of the first coefficient.

Dividers of constant term (10) are: 1, -1, 2, -2, 5, -5, 10, -10.
Dividers of first coeff. (5) are: 1, -1, 5, -5. So possible rational roots are:

\[\pm \frac{ 1,2,5,10 }{ 1,5 }\]

If you write these various possibilities as separate numbers (simplifying the fractions), you've got them all!