SOLUTION: I really need help I don't get what to do. For each equation, find the number of complex roots, the possible number of real roots, and list the possible rational roots. x^5-2x^2+5

Question 838611: I really need help I don't get what to do. For each equation, find the number of complex roots, the possible number of real roots, and list the possible rational roots. x^5-2x^2+5x-16=0 and if possible would this one be solved the same way
5x^4-15x+6=0
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The first one you ask is easier to handle, since coefficient on x^5 is 1. You just have integer zeros to check. (Read and study the Rational Roots Theorem.)

, rewrite using all the places values.
, and the dividend will be the left member.

The number of real zeros could be as many as 5, the same as the degree of the polynomial. The number of real zeros will not be more than 5.

Use synthetic division to check the possibility of any or each of 1, 2, 3, 6, -1, -2, -3, -6. Study how to use synthetic division from your textbook.

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Note: unless I made a couple of mistakes, no rational zeros found. The roots or zeros would be irrational or maybe complex with imaginaries.
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