Find all zeros of...

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
What have you tried? Do you know the factor theorem?

Start substituting values that are factors of \(\displaystyle -25 \) until you get a zero.
 
Dec 2009
200
35
Arkansas
Use the rational root theorem \(\displaystyle \frac{p}{q}=\frac{\textrm{factor of constant}}{\textrm{factor of leading coeff.}}\)

Use Descartes rules of signs to find how many roots you need, in order to know when to stop.

Then use synthetic division to check your answer (If the remainder is 0, then it is a root.)

If the number of roots found by descartes rule does not match the degree you might have to factor. OR! You can use synthetic division on the orginal polynomial by the roots, and the resulting equation will possibly give you a solvable equation (such as x^2+5, then \pm 5i)


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