SOLUTION: find the number of complex roots,the possible number of real rational roots x^7-2x^6+3x^2-2x+5=0 and 8-4x^3+4x^6=0

Question 38459This question is from textbook Algebra 2
: find the number of complex roots,the possible number of real rational roots
x^7-2x^6+3x^2-2x+5=0
and
8-4x^3+4x^6=0 This question is from textbook Algebra 2

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
x^7-2x^6+3x^2-2x+5=0
The highest power of x is 7. This is the degree or order of the equation. It also tells you that there are a total of 7 roots, if you include real roots, complex roots, and repeated roots. Complex roots will always be in conjugate pairs--i.e., two or four or six complex roots. Therefore, these are the possibilites.

7 real and no complex roots
5 real and two complex roots (one conjugate pair).
3 real and four complex roots (two conjugate pairs).
1 real and six complex roots (three conjugate pairs).

8-4x^3+4x^6=0
The highest power of x is 6, so there will be a total of 6 roots. These are the possibilities:
6 real roots and no complex roots
4 real roots and two complex roots (1 conjugate pair)
2 real and four complex roots (two conjugate pairs).
No real and six complex roots (three conjugate pairs).

R^2 at SCC

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