Ask Me Help Desk - I need to solve a 5th degree polynomial

$2x^{5}-17x^{4}+33x^{3}+23x^{2}-59x-30$

See this link: https://www.askmehelpdesk.com/math-s...ph-332062.html

You can graph it to find the roots or use the Rational Root Theorem as I explained in the link provided. I would suggest googling the Rational Root Theorem or finding it in any algebra text.

The possible roots are factors of -30 and 2. The constant and leading coefficient.

Possible roots:

Choices for the numerator c: $\pm 30, \;\ \pm 15, \;\ \pm 10, \;\ \pm 6 \;\ \pm 5, \;\ \pm 3 \;\ \pm 2, \;\ \pm 1$

Choices for the denominator d: $\pm 1 \;\ \pm 2$

Choices for c/d, which I will not list. You can see those from the other two lists.

Try dividing the poly by one of the choices, say, 2. Divide it by x-2, if it reduces to a fourth power poly, then that is a root. Continue on.
This one is nice because it has 5 real roots.